Edward  Bright 


ELEMENTARY-.  / 


PRACTICAL  PHYSICS 


A  GUIDE   FOR  THE   PHYSICAL   LABORATORY 


BY 

H.     N.     CHUTE,     M.S. 

Teacher  of  Physics  in  the  Ann  Arbor  High  School 


BOSTON,   U.S.A., 

D.   C.   HEATH   &   CO.,  PUBLISHERS. 
1890. 


C5 


Copyright,  1889 
BY    H.    N.    CHUTE 


JSockiuell  antJ 

BOSTON 


PREFACE. 


THIS  book  has  been  written  with  the  object  of  pro- 
moting the  teaching  of  Physics  by  what  is  known  as 
the  Laboratory  Method.  It  embodies  the  Experimental 
Course  which  has  been  found  suitable  for  students  of  the 
Eleventh  and  Twelfth  Grades  at  the  Ann  Arbor  High 
School,  where  the  author  has  had  several  years'  experi- 
ence in  conducting  large  laboratory  classes. 

It  consists  of  a  series  of  carefully  selected  exercises, 
both  qualitative  and  quantitative  in  character,  in  which 
full  directions  are  given  regarding  the  preparation  of  the 
apparatus,  and  the  manner  of  conducting  the  experi- 
ments, together  with  numerous  suggestions  about  methods 
of  observing,  note-taking,  and  making  inferences  from 
data.  The  work  is  not  designed  to  supplant  the  ordinary 
text-book,  as  definitions  and  statements  of  principles  have 
been  wholly  omitted  from  its  pages.  It  is  recommended 
that  the  study  of  some  suitable  elementary  treatise  on 
Physics  be  carried  on  in  the  usual  way,  the  teacher  per- 
forming in  the  presence  of  the  class  either  the  experi- 
ments therein  described  or  equivalent  ones  selected  from 
this  guide.  Such  instruction  should,  in  the  opinion  of 
the  author,  precede  the  introduction  of  the  student  to  the 

«— **         797967     . 


IV  I'REFACE. 

It  is  a  mistaken  supposition,  unfortunately  prevailing 
largely  among  science  teachers,  that  the  Laboratory 
Method  requires  a  student  to  discover  for  himself  the 
important  laws  and  truths  of  the  physical  world.  The 
race  has  been  centuries  in  reaching  its  present  knowledge 
of  Nature's  laws,  and  it  is  evidently  unreasonable  to 
expect  the  untrained  mind  of  a  boy  or  girl  to  discover 
and  formulate  in  one  year,  or  even  in  several  years,  the 
principles  discussed  in  an  elementary  book  on  Physics. 
The  office  of  the  school  physical  laboratory  is  not  one  of 
original  discovery;  but,  in  the  first  place,  to  put  the 
student  in  the  best  possible  position  to  see  what  he  looks 
at,  in  order  that  fact-knowledge  may  be  added  to  word- 
knowledge  in  the  most  impressive  way  by  having  the 
head  and  hand  work  and  learn  together ;  and,  in  the 
second  place,  to  train  the  faculties  to  exactness  of  obser- 
vation, independence  and  carefulness  in  forming  conclu- 
sions, and  good  judgment  in  weighing  evidence. 

It  is  not  necessary,  neither  is  it  advisable,  that  the 
whole  subject  of  Physics  be  studied  in  a  didactic  way 
before  a  student  enters  on  his  experimental  work.  All 
that  is  required  is  that  the  class  instruction  on  any  sub- 
ject or  topic  shall  precede  the  student's  study  of  that 
subject  experimentally,  for  it  will  be  found  that  only  in 
this  way  will  the  complete  significance  of  the  experiment 
and  its  results  be  fully  perceived,  and  intelligent  work 
secured  to  the  exclusion  of  that  which  is  lifeless  and 
mechanical.  No  fear  need  be  entertained  that  the 


P  BE  FACE.  V 

student's  interest  will  be  lessened  in  the  least  by  a 
knowledge  of  what  he  is  likely  to  see,  obtained  either 
from  seeing  the  experiment  performed  by  the  teacher  or 
from  reading  about  it  in  the  class  manual.  The  author's 
experience  for  a  number  of  years  has  convinced  him  that 
the  opposite  effect  is  almost  invariably  produced;  that  is, 
a  livelier  and  more  intelligent  interest  is  kindled  thereby. 
The  student  always  finds  that  the  close  contact  with  the 
experiment  in  the  laboratory  reveals  to  him  enough  that 
he  did  not  see  when  he  witnessed  it  in  the  class-room,  or 
found  no  mention  of  in  the  manual  he  consulted,  to  com- 
pensate him  many  times  over  for  the  time  he  now  has 
put  upon  it. 

There  is,  however,  a  large  class  of  experiments  that 
cannot  be  performed  to  any  advantage  outside  of  the 
laboratory,  particularly  those  of  a  quantitative  character, 
involving  the  verification  of  physical  laws  and  the  deter- 
mination of  physical  constants.  On  these  subjects  but 
little  help  is  furnished  by  the  ordinary  text-books,  and 
students  graduate  every  year  from  our  High  Schools  and 
Colleges  absolutely  ignorant  of  the  difficulties  in  the  way 
of  accurately  determining  the  simplest  physical  constant, 
or  establishing  the  truth  of  the  most  familiar  physical  law. 
To  experiments  of  this  kind  special  attention  has  been 
given  in  these  pages,  for  it  is  believed  that  it  is  only  by 
doing  this  so-called  "  dead-work  "  can  a  student  ever  come 
to  a  correct  and  complete  understanding  of  these  laws. 
The  objection  that  such  work  is  beyond  the  students  who 


VI  PREFACE. 

ordinarily  study  physics  in  our  High  Schools  is  fully  met 
by  the  fact  that  the  data  appended  to  Exercises  275  and 
276  of  this  book  were  taken  from  the  note-books  of  two 
young  girls  who  had  no  other  aid  than  that  furnished  in 
the  problems  as  given  there. 

Although  in  the  directions  accompanying  the  exercises 
considerable  attention  is  given  to  the  construction  of  ap- 
paratus, the  author  would  not  be  understood  as  approving 
of  converting  the  physical  laboratory  into  a  mechanical 
work-shop.  The  object  in  giving  so  many  details  was 
threefold.  First,  to  make  it  possible  for  schools,  having 
but  little  means  for  purchasing  apparatus,  to  get  together, 
in  time,  through  the  aid  of  teacher,  students,  and  local 
mechanics,  a  supply  of  apparatus  that  has  the  one  great 
merit,  "  it  seldom  fails  to  do  that  which  is  required  of 
it."  Secondly,  to  show  that  the  verification  and  the  illus- 
tration of  Nature's  great  laws  require  no  elaborately  fin- 
ished and  expensively  constructed  appliances;  but  that, 
on  the  contrary,  the  more  simple  and  inexpensive  the 
mechanism  is,  the  more  satisfactory  is  usually  its  per- 
formance. Thirdly,  to  give  the  student  as  clear  an  idea 
as  possible  of  the  instrument  placed  in  his  hands  by 
putting  before  him  the  specifications  followed  in  its  con- 
struction. The  author  well  remembers  that  no  study  of 
books  ever  gave  him  as  clear  an  idea  of  the  induction 
coil  as  he  got  from  a  working-drawing  and  specifications 
of  one  published  several  years  ago  in  a  well-known  scien- 
tific periodical. 


PEEFACE.  VII 

Special  attention  is  called  to  the  appendices.  In  the 
first,  the  author  has  attempted  to  outline  a  method  of  con- 
ducting laboratory  work :  the  equipment  of  a  room,  the 
selection  of  apparatus,  and  the  management  of  large 
classes  with  limited  facilities  are  some  of  the  topics  dis- 
cussed at  considerable  length.  In  the  second  appendix 
there  is  described  a  large  number  of  operations,  such  as 
teacher  and  student  are  often  called  on  to  perform,  in  re- 
pairing, constructing,  and  adjusting  apparatus.  Many 
very  valuable  recipes  find  a  place  there,  all  of  which  have 
been  thoroughly  tried,  and  are  known  to  be  most  excel- 
lent. In  the  third  appendix  is  given  a  very  complete  list 
of  such  Constants  as  will  be  needed  or  found  convenient 
in  the  application  of  the  truths  of  Physics  to  the  solution 
of  practical  problems.  They  will  also  serve  as  guides 
to  the  student,  often  indicating  to  him  what  degree  of 
accuracy  he  has  secured  in  his  experimentation. 

It  is  too  much  to  expect  that  these  pages  will  be  found 
free  from  errors ;  still  it  is  believed  that  a  fair  degree  of 
accuracy  has  been  secured.  Dr.  T.  C.  Mendenhall,  Presi- 
dent of  the  Rose  Polytechnic  Institute,  has  carefully  and 
critically  read  the  whole  work  in  manuscript  and  in  proof, 
and  has  contributed  many  valuable  suggestions.  The  fol- 
lowing well-known  science  teachers  have  also  carefully 
read  the  work  in  proof,  and  aided  very  greatly  in  giving 
it  its  present  degree  of  accuracy  and  completeness  of 
treatment:  W.  Le  Conte  Stevens,  Packer  Collegiate  In- 
stitute, Brooklyn,  N.  Y. ;  J.  Montgomery,  Kalamazoo  Col- 


VIII  PREFACE. 

lege,  Kalamazoo,  Mich. ;  E.  P.  Jackson,  Latin  School, 
Boston,  Mass. ;  J.  Y.  Bergen,  Latin  School,  Boston, 
Mass. ;  James  H.  Shepard,  Agricultural  College,  Brook- 
ings,  Dak.  ;  George  B.  Merriman,  Rutgers  College,  New 
Brunswick,  N.  J. ;  J.  H.  Pillsbury,  Smith  College,  North- 
ampton, Mass. ;  George  N.  Cross,  Exeter  Academy,  Exe- 
ter, N.  H. ;  George  I.  Hopkins,  High  School,  Manchester, 
N.  H.;  A.  C.  Boyden,  Normal  School,  Bridgewater,  Mass.; 
George  L.  Chandler,  High  School,  Newton,  Mass. ;  Albert 
C.  Hale,  Boys'  High  School,  Brooklyn,  N.  Y. ;  Arthur  M. 
Mo  wry,  High  School,  Salem,  Mass. ;  and  many  others. 

Special  acknowledgments  are  due  to  A.  P.  Gage,  of 
Boston,  James  W.  Queen  and  Co.,  Philadelphia,  and  E.  S. 
Ritchie  and  Sons,  of  Brookline,  Mass.,  for  the  use  of 
a  number  of  illustrations.  The  author  would  also  ac- 
knowledge his  indebtedness  to  that  great  company  of 
scientific  workers  who  have  furnished  him,  through  their 
writings,  with  the  material,  and  sometimes  with  the 
words,  for  the  pages  which-  follow.  Should  this  imperfect 
effort  prove  itself  helpful  to  that  large  body  of  earnest 
men  and  women  who  are  striving  to  solve  the  great 
problem  of  "  what  is  the  best  method  of  science  teaching," 
the  author  will  feel  fully  repaid  for  the  many  laborious 
hours  of  day  and  night,  in  laboratory  and  in  study,  he 
has  spent  for  a  number  of  years  in  collecting,  verifying, 
selecting,  and  adjusting  the  matter  contained  in  the 
laboratory  guide  which  he  now  offers  to  the  teaching 
profession. 


TO    THE    TEACHER. 

I. 

HOW    TO    USE   THIS    MANUAL. 

1.  The  plan  on  which  this  book  is  prepared  does  not 
restrict  it  to  any  particular  theory  of  practical  science 
teaching.  If  you  believe  that  a  full  course  of  didactic  in- 
struction should  precede  the  admission  of  students  into  the 
laboratory,  and  that  the  practical  work  should  be  entirely 
quantitative,  then  omit  the  qualitative  and  select  from  the 
quantitative  such  as  is  adapted  to  your  wants.  On  this 
plan,  however,  it  will  generally  be  found  very  difficult  to 
handle  large  classes,  as  it  necessarily  crowds  all  the  prac- 
tical work  into  a  small  part  of  the'  school  year,  rendering  it 
nearly  impossible  to  arrange  a  programme  which  provides 
enough  hours  per  week  for  each  student  to  enable  him  to 
accomplish  much.  It  would  be  better  to  organize  the 
laboratory  work  a  week  or  so  after  the  class-room  work 
has  begun,  and  carry  on  the  two  simultaneously.  The 
didactic  instruction  will  by  this  plan  be  in  advance  of  the 
practical  work  sufficiently  to  enable  the  student  to  carry 
on  his  work  intelligently.  About  three  hours  per  week 
devoted  to  class  recitations  on  some  good  text-book,  accom- 


X  TO   THE   TEACHER. 

panied  by  illustrative  experiments  by  the  teacher ;  two  to 
six  hours  per  week  spent  in  practical  work  in  the  labora- 
tory ;  and  one  hour  per  week  spent  by  students  in  class, 
discussing  and  comparing  their  reports  on  this  work,  is  the 
plan  on  which  the  author  has  taught  physics  for  several 
years  with  results  that  are  quite  satisfactory. 

2.  If,  on  the  other  hand,  you  believe  that  the  experi- 
mental work  should  precede  that  of  the  class-room,  a  view 
held  by  many  of  our  ablest  teachers,  you  will  find  that  the 
Guide  contains  a  very  complete  collection  of  experiments, 
from  which  you  can  select  those  adapted  to  your  facilities. 
These  experiments  are  accompanied  by  hints  on  observing, 
recording  observations,    and   correctly   interpreting    data 
obtained,  so  that  the  labor  of  supervision  will  be  greatly 
reduced,  and  the  burden  of  preparing  the  work  reduced  to 
a  minimum. 

3.  It  will  not  interfere  with  the  plan  of  the  book  to 
omit  any  exercise  not  adapted  to  the  laboratory  facilities. 
It  is  best  to  assign  work  to  the  student  that  he  has  the 
genius   requisite   to    do   something  with.     See  Art.   596. 
The  large  variety  of  material  from  which  to  choose  will 
make  it  possible  to  make  changes  each  year.     Old  note- 
books will  be  of  less  value  to  new  classes  if  this  is  done. 

4.  It  may,   occasionally,   be  found  desirable  to  make 
changes  in  a  problem  to  adapt  it  to  a  piece  of  apparatus 
of  different  design  from  that  contemplated  in  the  Guide. 
These  changes  may  be    explained  in    the    work-room  or 
class-room,  as  found  most  convenient. 


TO   THE  TEACHER.  XI 

5.  Require   students  to  use  reference  books  freely  in 
studying  their  practical  work.     Also  encourage  them  to 
make  changes  in  the  mode  of  procedure.     See  Art.  599, 
Rule  4.     It  will  not  unfrequently  happen  that  a  student 
will  hit  on  some  little  modification  that  will  enable  him  to 
secure  much  more  accurate  resiilts,  mainly  for  the  reason 
that  he  devised  it,  and  therefore  could  handle  it  all  the 
better  on  that  account. 

6.  It  will  be  seen  that  the  book  seldom  states  what  the 
results  should  be.     Experience  has  convinced  the  author 
that  more  independent  and  honest  work  can  be  secured  on 
this  plan.     Let  the  average  student  take  the  ordinary  text- 
book  into  the  laboratory  and  work  through  one    of   its 
experiments,  and  in  the  majority  of  cases  he  will  believe 
that  he  got  exactly  what  the  book  account  said  he  would, 
nothing  more  and  nothing  less,  notwithstanding  the  fact 
that  half  of  our  book-makers,  according  to  Prof.  Tyndall, 
describe    experiments  which   they  never   made,  their  de- 
scriptions often  lacking  both  force  and  truth. 

II. 

HOW   TO   SECURE   APPARATUS. 

1.  It  is  a  mistake  to  suppose  that  practical  work  with 
large  classes  necessitates  a  large  and  expensive  collection 
of  apparatus.  The  cost  of  equipping  a  Physical  Labora- 
tory is  less  than  is  generally  supposed.  Nearly  every  school 


XII  TO    THE   TEACHER. 

already  possesses  the  pieces  that  are  expensive,  as  air- 
pump,  electrical  machine,  and  their  many  accessories. 
When  the  author  decided  to  introduce  the  Laboratory 
Method  in  the  Ann  Arbor  High  School,  he  asked  the 
School  Board  to  do  three  things :  furnish  a  room  with 
gas,  water,  and  a  few  flat-top  tables ;  appropriate  $100  to 
purchase  a  few  of  the  simpler  devices  for  making  accurate 
measurements;  and  require  each  student  to  pay  each  term 
a  small  fee,  the  proceeds  to  be  devoted  to  enlarging  the 
equipment.  The  work  began  with  over  eighty  students, 
and  now  for  several  years  not  a  dollar  has  been  asked  of 
the  School  Board  for  purchasing  apparatus ;  still  the 
facilities  are  rapidly  improving  each  year,  and  are  probably 
superior  to  those  of  most  schools  of  the  kind. 

2.  In  Art.  595  are  given  many  hints  regarding  appa- 
ratus. 

3.  The  majority  of  teachers  have  but  little  time  to  give 
to  the  construction  of  apparatus ;  still,  in  most  cases,  some- 
thing can  be  done,  especially  in  putting  things  together 
that  were  prepared  by  some   mechanic.     There  is   such 
work  as  winding  the  wire  on  galvanometer  frames  and 
making  the  needles  for  the  same,  winding  electro-magnets 
and  magnetizing  steel  magnets  made  by  a  local  blacksmith, 
etc.     School  Boards  are  not  easily  induced  to  appropriate 
money  to  be  expended  outside  of  the  district,  but  they 
will  generally  be  found  willing  to  employ  a  carpenter  for 
a  few  days  to  work  for  the  school.     There  are   a  great 
many  devices  described  in  these  pages  that  such  a  man 


TO   THE  TEACH  EM.  X11I 

can  make,  and  just  as  satisfactorily  as  if  he  lived  in  some 
distant  city.  These  instruments  may  require  adjustment, 
a  statement  true  of  90  per  cent,  of  all  apparatus  purchased 
of  the  most  noted  makers. 

4.  Europe  is  the  great  storehouse  of  cheap  apparatus, 
and  under  the  law,  schools  can  import  for  their  own  use 
duty  free.  In  this  way  a  saving  of  30  to  50  per  cent,  can 
often  be  effected.  This  is  especially  true  in  the  matter  of 
lenses,  Grenet  batteries,  balances,  weights,  etc.  This  im- 
porting can  be  done  through  any  of  the  firms  referred  to 
in  Art.  596. 

III. 

HOW   TO   MANAGE   THE   LABORATORY. 

1.  There  are  in  use  two  methods  of  conducting  labora- 
tory work,  known  as  the  separate  system  and  the  collective 
system.  Under  the  former  each  section  of  two  students 
would  work  on  different  problems,  the  apparatus  going 
around  in  rotation.  It  is  difficult,  under  this  plan,  to  have 
the  student's  work  conform  to  a  strictly  logical  order,  but 
it  requires  little  or  no  duplication  of  apparatus.  The 
collective  system  is  the  ideal  one.  Under  it  all  are  engaged 
on  the  same  work  at  the  same  time.  It  has  this  advantage 
over  the  separate  system,  a  teacher  can  instruct  all  at  once 
on  any  point  demanding  more  than  ordinary  care,  and  will 
have  more  time  to  devote  to  the  few  who  may  be  less  apt 
in  their  work.  The  author  would  recommend  a  combining 


XIV  TO   THE  TEACHER. 

of  the  two  methods  as  better  adapted  to  the  circumstances 
of  most  schools.  This  would  involve  a  duplication  of 
those  appliances  which  are  less  expensive,  as  thermometers, 
lenses,  mirrors,  galvanometers,  etc. 

2.  In  Arts.  596,  597,  and  599  will  be  found  quite  full 
directions  and  suggestions  on  conducting  practical  work. 
Those  which  relate   to  order  are  very  important.      The 
student  should  understand  that  the  work-room  is  not  a 
play-room,  and  that  every  moment  of  his  time  must  be  put 
to  good  use. 

3.  By  arranging   the    school   programme   so  that  stu- 
dents   taking   physics    have    all   their   recitations   in   the 
forenoon,  it  will  be  possible  for  them  to  devote  at  least  two 
of  their  afternoons  to  the  laboratory  each  week.     If  pos- 
sible two  consecutive  hours  should  be  spent  there,  for  it 
will  not  unfrequently  happen  that  one   hour  will  be  too 
short  to  complete  a  line  of  investigation,  and  to  stop  when 
not  through  is  to  lose  all  that  has  been  done. 

4.  It  is  recommended  that,  generally,  two  students  be 
permitted  to  work  together  on  the  same  problem,  as  more 
than  two  hands  are  often  required  in  performing  an  experi- 
ment.     This  plan  will  increase  the  number  of   students 
who  can  be  kept  at  work.     It  is  doubtful  if  one  person 
can  look  properly  after  more  than  twelve  students,  and 
when  large  numbers  necessitate  admitting  many  more  than 
this  number  to  the  room  an  assistant  should  be  employed. 

5.  If  the  students  have  definite  places  assigned  them 
in  the  room  it  will  conduce  to  good  order.     Each  student 


TO    THE   TEACHER.  XV 

should  be  held  responsible  for  the  apparatus  put  at  his 
disposal,  and  if  broken  or  in  any  way  injured  through  his 
fault  he  should  be  required  to  make  it  good. 

6.  The  work  expected  each  week  from  the  student 
should  be  assigned  him  a  few  days  in  advance,  and  he 
should  be  required  to  give  it  careful  study  before  reporting 
for  duty,  in  order  that  he  may  not  be  hampered  by  igno- 
rance of  the  successive  steps  in  the  experiment.  The 
author  does  not  believe  it  is  wise  to  restrict  all  experiments 
to  those  of  a  quantitative  character.  He  would  require 
the  student  to  repeat  for  himself  many  of  the  experiments 
of  the  class-room,  with  the  object  of  bringing  him  into 
actual  contact  with  the  things  themselves,  so  that  their 
properties  and  relations  may  become  familiar  as  solid,  first- 
hand mental  acquisitions.  Furthermore,  there  are  many 
important  truths,  the  establishment  of  which  involves  no 
exact  measurements,  that  cannot  be  developed  experiment- 
ally in  the  class-room  without  expensive  apparatus,  whereas 
a  very  simple  device  placed  in  the  student's  hands  will 
enable  him  to  see  the  whole  matter  clearly. 


IV. 

HOW  TO  SHORTEN  THE  COURSE. 

1.  As  is  implied  in  more  than  one  place,  this  book  con- 
tains much  more  work  than  a  student  can  master  in  the 
time  usually  devoted  to  the  subject.  There  is  no  reason 


XVI  TO    THE   TEACHER, 

why  a  teacher  should  not  omit  any  exercise  or  set  of  exer 
cises  he  dhooses.  It  was  thought  advisable  to  have  the  book 
fairly  complete  in  its  treatment  of  each  subject,  that  it 
might  the  better  meet  the  wants  of  the  greater  number, 
as  it  often  happens  that  what  is  adapted  to  the  needs  of 
one  school  is  not  to  those  of  another.  All  subjects,  how- 
ever, are  not  equally  important,  and  circumstances  will 
often  compel  the  omission  of  certain  questions.  The  author 
would  suggest  that  generally  the  following  topics  might 
be  omitted  without  seriously  detracting  from  the  value  of 
the  course :  Sees.  III.,  IV.,  V.,  VI.,  VIII.,  X.,  and  XI.  of 
Chap.  I . ;  VII.  of  Chap.  III. ;  IX.  of  Chap.  IV. ;  XV.,  XVI., 
and  XVII.  of  Chap.  V. ;  VII.,  XVI.,  XVII.,  and  XVIII.  of 
Chap.  VI. ;  X.,  XI.,  and  XIII.  of  Chap.  VII.  From  the 
other  sections  select  such  experiments  as  bring  out  most 
satisfactorily  with  the  apparatus  at  command  the  principles 
th&y  are  designed  to  teach.  Under  many  exercises  are 
found  several  methods  of  accomplishing  the  same  thing. 
It  adds  interest  to  the  work  to  assign  different  methods 
to  different  students  and  have  them  compare  results. 

2.  If  both  time  and  appliances  are  limited,  a  still  further 
contraction  is  possible,  and  in  that  case  the  author  recom- 
mends that  some  such  selection  as  suggested  in  Art.  596 
be  made.  This  principle  should  govern  the  work  at  all 
times;  a  few  experiments  thoroughly  studied  will  be  much 
more  instructive  than  a  great  many  superficially  and  hastily 
gone  over. 


CONTENTS. 


CHAPTER   I. 

PAGE 

THE  PROPERTIES  OF  MATTER  EXPERIMENTALLY  DETERMINED  .  1-68 
I.     Extension.  —  Measurements    of    Length,    Area, 

and  Volume    .......  1-22 

II.     Estimation  of  Mass 23-32 

III.  Impenetrability      .......  33-36 

IV.  Divisibility 36-38 

V.     Porosity 38-41 

VI.     Indestructibility 41-44 

VII.     Cohesion 44-50 

VIII.     Elasticity       ........  50-54 

IX.     Capillary  Action 55-60 

X.     Solubility       . 61-62 

XI.     Diffusion 63-68 


CHAPTER  II. 

MECHANICS  OF  SOLIDS         .                  69-100 

I.     Laws  of  Motion     .......  69-77 

II.     Centre  of  Mass.  —  Stability           ....  77-80 

III.  Curvilinear  Motion        ......  80-82 

IV.  Accelerated  Motion.  —  Gravitation. — Projectiles,  83-92 
V.     The  Pendulum 92-96 

VI.     Friction 96-97 

VII.     The  Simple  Machines 97-100 

XVII 


XVIII  CONTENTS. 

CHAPTER   III. 

MECHANICS  OF  FLUIDS 101-126 

I.     Pressure  in  Fluids 101-108 

II.     Law  of  Boyle         .......  108-110 

III.  Law  of  Pascal 110-113 

IV.  The  Siphon  and  Pump 113-116 

V.     The  Principle  of  Archimedes        .         .         .         .116-119 

VI.     Determination  of  Density 120-126 

CHAPTER   IV. 

HEAT 127-169 

I.     Heat,  and  Mechanical  Motion       ....  127-132 

II.     Heat  and  Chemical  Action 132 

III.  Conduction  of  Heat 133-136 

IV.  Convection  of  Heat 136-139 

V.     Expansion  by  Heat HO-H5 

VI.     Thermometry 146-152 

VII.     Radiant  Heat 153-159 

VIII.     Calorimetry 160-167 

IX.     Artificial  Cold 167-169 

CHAPTER  V. 

MAGNETISM  AND  ELECTRICITY 170-237 

I.     Magnets.  —  Polarity.  —  Induction          .         .         .  170-173 

II.     Nature  of  Magnetism 173-174 

III.  The  Magnetic  Field 174-179 

IV.  Terrestrial  Magnetism  ......  179-180 

V.     Frictional  Electricity 180-184 

VI.     Statical  Induction 184-186 

VII.     Electrical  Distribution 187-190 

VIII.     Condensers     . 190-193 

IX.     Electrical  Machines       .         .         .         .         .         .  193-196 

X.     Voltaic  Electricity. —The  Battery       .         .         .  196-199 

XL     Effects  of  Electrical  Currents       ....  200-204 

XII.     Electrical  Measurements        .  204-221 


CONTENTS. 


XIX 


MAGNETISM  AND  ELECTRICITY.  —  Continued.  PAGE 

XIII.  Electro-Magnetism  and  Electro-Dynamics    .         .  221-227 

XIV.  Current  Induction 227-232 

XV.  Luminous  Effects           ......  233-236 

XVI.  Therrao-Electricity         .         .         .         .         .         .  236-237 

CHAPTER   VI. 

SOUND 238-282 

I.  Wave  Motion          .......  238-241 

II.  Sources  of  Sound          ......  241-244 

III.  Transmission  of  Sound          .....  244-245 

IV.  Velocity  of  Sound          ......  245-248 

V.     Propagation  of  Sound 249-250 

VI.     Reflection  of  Sound 250-252 

VII.  Refraction  of  Sound     .         .         .         .         ...  252 

VIII.     Loudness  of  Sound 253-256 

IX.     Interference  of  Sound 256-258 

X.     Sympathetic  Vibrations 258-260 

XI.     Pitch  of  Sound 261-262 

XII.  Laws  of  Vibrating  Rods  and  Strings  .         .         .  263-266 

XIII.  Overtones 266-267 

XIV.  Laws  of  Sounding  Air-Columns  ....  268-270 
XV.  Harmony  and  Discord  ......  270-271 

XVI.     Vibrating  Plates  and  Bells 271-273 

XVII.  Attraction  of  Vibrating  Bodies     ....  273 

XVIII.  Graphic  and  Optical  Study  of  Sound  .         .         .  273-281 

XIX.     Vocal  Organs 282 

CHAPTER   VII. 

LIGHT  .                  283-333 

I.     Sources  of  Light 283-286 

II.  Rectilinear  Propagation  of  Light          .         .         .  287-289 

III.  Photometry    .         . 289-291 

IV.  Reflection  of  Light 291-297 

V.     Mirrors 297-305 

VI.  Single  Refraction  of  Light  .         .         0         .         .  305-309 

VII.  Lenses    .        .  309-314 


XX 


CONTENTS. 


LIGHT.  —  Continued. 

VIII.  Dispersion 

IX.  Color 

X.  Spectrum  Analysis         ..... 

XI.  Interference  of  Light  ..... 

XII.  Optical  Instruments       ..... 

XIII.  Double  Refraction  and  Polarization  of  Light 


APPENDICES. 


A. — The  Physical  Laboratory 

B.  —  Laboratory  Operations 

C.  —  Tables  for  Reference 


PAGE 

314-317 
317-320 
320-323 
324-325 
325-328 
329-333 


337-353 
354-360 
361-376 
.  361 
.  361 
.  364 
.  364 


I.     Capillarity 

II.  Densities  of  Various  Substances     .... 

III.  Limit  of  Elasticity 

IV.  Electrical  Conductivity 

V.  Approximate    Electro-motive   Force    of    Primary   Bat- 
teries         .........  365 

VI.  Electrical   Resistance,  Diameter,  etc.,  of  Pure  Copper 

Wire 365 

VII.     Acceleration  due  to  Gravity 367 

VIII.  Heat,    Absorbing,     Conducting,    Radiating,    Reflecting 

Power 367 

IX.  Boiling-points  of  Substances  at  Bar.  Pres.  76  cm.       .  368 

X.     Coefficients  of  Expansion 368 

XI.  Latent  Heat  of  Liquefaction  and  Vaporization      .  369 

XI  [.     Melting  Points 369 

XIII.  Specific  Heat 370 

XIV.  Indices  of  Refraction 370 

XV.     Mensuration  Rules 371 

XVI.     Length  of  Seconds'  Pendulum 371 

XVII.     Velocity  of  Sound  at  0°  C 372 

XVIII.     Elasticity  of  Traction .372 

XIX.     Tenacity 373 

XX.  Trigonometrical  Functions      ......  373 

XXI.  Some  Useful  Numbers   .         .         .         .         .         .         .  375 

XXII.  Weights  and  Measures  .                           ....  375 


PEACTICAL    PHYSICS. 


CHAPTER    I. 

THE    PROPERTIES   OF   MATTER    EXPERIMENTALLY 
DETERMINED, 

I.    EXTENSION.  — MEASUREMENTS    OF    LENGTH,    AREA, 
AND    VOLUME. 

1.  Apparatus.  —  The   fundamental   principle  involved  in 
all    measurements    is    that    of    direct    comparison   with   some 
assumed  standard,  the  accuracy  of  the  results  depending  upon 
that  of  the  standard,  and  the  methods  adopted  to  insure  close 
comparisons.     Among  the  many  instruments  employed  in  this 
kind  of  investigation  may  be  mentioned  the  Dividers,  Diagonal 
Scale,  Metre-Rod,  Verniered  Steel  Caliper,  Micrometer  Caliper, 
Spherometer,  Outside  and  Inside  Caliper,  Graduated  Measure, 
Beam  Compass,  Proportional  Dividers,  Protractor,  etc.     These 
are  described  in  the  following  articles   of   this  section,  their 
methods   of    use   explained,   and   in   many   cases   simple   and 
efficient  substitutes  suggested. 

2.  Exercise.  —  Measure  the  distance  between  two  points 
situated  on  any  plane  surface,  as  a  sheet  of  brass  or  card- 
board. 

I 


*<  PRACTICAL   PHYSICS. 

This  can  be  done  with  sufficient  accuracy  by  means  of  a  pair 
of  Dividers  (Fig.  1)  and  a  Diagonal  Scale  (Fig.  3).  Spring 
Dividers  (Fig.  2)  are  preferable.  Any  accurately  and  finely 
divided  scale  can  be  used  ;  but  of  cheap  scales,  the  diagonal 
scale,  boxwood  or  ivory,  is  the  most  suitable  for  this  problem. 

Open  the  dividers,  and  place  one  of  its  points  exactly  on  one 
of  the  given  points  on  the  plane  surface,  and  the  other  point 
on  the  second  given  point.  Now  place  one  point  of  the  dividers 
at  one  of  the  divisions  1,  2,  3,  etc.,  of  the  scale,  as  2, 
being  careful  to  select  one  that  will  cause  the  other  point 
to  fall  at  0,  or  between  0  and  the  vertical  line  bounding 
the  scale.  If  the  right-hand  point  falls  at  0, 
then  the  required  distance  is  2  units.  If  the 
right-hand  point  falls  to  the  right  of  0,  as  at 
the  diagonal  line  3,  then  the  distance  is  2.3 
units.  If  the  right-hand  point  falls  between 
two  of  these  diagonal  lines,  as  3  and  4,  then 
move  the  dividers  toward  the  opposite  edge  of 
the  scale,  keeping  the  line  of  the  points  parallel 
to  the  lines  running  lengthwise  of  the  scale, 
FIG.  i.  and  at  the  same  time  the  left-hand  point  in  FIG.  2. 
the  line  2,  until  the  right-hand  point  meets  the  intersection  of 
a  diagonal  line  with  a  horizontal  one.  Should  such  a  point 
be  where  the  diagonal  line  3  intersects  the  horizontal  one  7, 
then  the  distance  is  2.37  units.  This  multiplied  by  the  value 
of  the  scale  unit,  expressed  either  in  inches  or  centimetres,  will 
give  the  absolute  length. 

In  conveying  the  measurements  to  the  scale,  there  is  danger 
that  the  dividers  may  get  closed  up  a  little  from  pressure  of 
the  fingers  in  holding  the  instrument.  This  must  be  carefully 
guarded  against.  Again,  the  points  of  the  dividers  must  be 
placed  with  accuracy  on  the  given  points,  and  no  pressure 


TEE   PROPERTIES   OF  MATTER. 


3 


applied  that  would  be  likely  to  indent  the  surface  in  the  least. 
Several  independent  measurements  must  always  be  made ; 
then,  by  adopting  their  arithmetical  mean,  a  result  differing 
less  from  the  exact  one  is  more  likely  to  be  obtained.  These 


30 


40 


50 


0246 


different  measurements  should  all  be  neatly  and  accurately 
recorded  at  the  time  they  are  made,  in  a  suitable  note-book 
provided  for  the  purpose,  observing  some  such  plan  as  the 
following :  — 


LINEAR    MEASUREMENTS. 


Problem. —Determination  of  distance  between  two  points  on  card- 
board.    Sept.  5,  1888. 

Method.  —  Dividers  and  scale. 
Results.  — 

First  measurement 

Second         "  .    „ 

Third  " 


Mean 

Mean  in  cm 

Value  of  scale  unit  .    . 


4  PRACTICAL   PHYSICS. 

3.  Exercise.  —  Draw  on  paper  three  straight  lines  whose 
lengths   are   respectively   2.34  inches,   3.57  inches,   and  1.89 
inches. 

4.  Exercise.  —  Cut  a  circle,  as  accurately  as  possible,  from 
cardboard.     Measure  its  circumference  by  rolling  it  along  a 
straight  line  drawn  on  paper.     Measure  its  diameter,  and  com- 
pute the  ratio  of  the  circumference  to  the  diameter. 

A  pair  of  dividers  and  a  diagonal  scale  will  be  found  con- 
venient for  the  purpose. 

Make  several  independent  measurements  and  record  the 
results. 

The  record  may  be  made  as  follows  :  — 

Problem.  —  Determination  of  the  ratio  of  the  circumference  of  a 
circle  to  its  diameter.  Sept.  5,  1888. 

Method.  —  Dividers  and  diagonal  scale. 

Results.  — 

Circumference.  Diameter. 

First  measurement     ... 
Second         "  ... 

Third  " 


Mean 

Ratio, Error, Per  cent  of  error, 

The  error  is  the  difference  between  the  ratio  obtained  and  the  true  value,  3.1416. 

5.  Exercise.  —  Measure  the  length  and  the  breadth  of  one 
of  the  tables  in  the  room,  employing  both  the  P^nglish  and  the 
French  measure.  Reduce  each  to  the  other,  then  compare  and 
point  out  in  how  many  ways  the  differences  in  the  final  results 
may  be  accounted  for. 


THE  PROPERTIES   OF  MATTER. 


The  metre-rod,  such  as  is  furnished  by  the  American  Metric 
Bureau,  is  a  suitable  instrument  for  solving  this  problem.  The 
results  may  be  recorded  as  follows  :  — 

Problem.  —  Determination  of  the  length  and  breadth  of  laboratory 
table  No.        .     Sept.  5,  1888. 
Method.  —  The  metre-rod. 
Results.  — 

Length.  Breadth. 

First  measurement    .     .  cm. in.  cm.       ..in. 

Second        "  .     . 

Third 


Mean 

Reduced     . 
Difference . 


6.   Exercise.  —  Measure  the  length  of  a  short  rod  or  bar 
of  wood  or  metal. 


miiiiiiliiiiliiiiliiiiliiiiliiiiliiiiliiiiliiiiliMiliiii'iiiiiii 

j  Dartir-g,  Ero-vp&  StiArpe.Pl-OTida'.CE.  R.I 


liliiiiliiiiliiiiliiiiliiiili 

|llll!llllll!lll|!|ll|l![ll! 

1 

JF 

gEgt 

c 

FIG 

...        ^ 

If  great  accuracy  is  required,  it  will  be  necessary  to  employ 
some  such  instrument  as  the  Verniered  Steel  Caliper,  an 
appliance  so  constructed  that  measurements  as  small  as  fiftieths 
of  a  millimetre  can  be  made  by  its  aid.  Figs.  4,  5,  and  6 
exhibit  some  of  the  forms  given  it ;  the  latter  being  without 
the  Vernier,  a  device  for  estimating  fractional  parts  of  the 


6 


PRACTICAL   PHYSICS. 


smallest  division  on  the  scale.  Where  the  verniered  form 
cannot  be  had,  for  financial  reasons,  this  simpler  form  may  be 
used  instead,  generally  with  sufficient  accuracy,  if  the  fractional 
parts  of  the  divisions  are  carefully  estimated  by  the  eye. 


i"" 

lll[l!ll|lllllllll|llll|lll!|!li:j 
'L... 

Wl  I  1  1  i  !  I 

'^   'a|    '    '    '    '    1    'so1 

°T'i  .1.1,1.  ill.  hi 

'I'M 

u    aa    •*             L, 

_i[j  

•I 

h_ 

_r 

FIG.  5 

""•^ 

To  measure  the  rod,  unclamp  the  screws  A  and  B  (Fig.  4), 
and  slide  the  jaw  C  away  from  D,  so  that  the  rod  can  be 
placed  between  C  and  D,  with  its  axis  parallel  to  the  bar  of 
the  caliper.  Then  clamp  A,  and  move  the  jaw  C  by  the  slow- 


FIG.  6. 

motion  screw  E  till  the  rod  is  just  firmly  held  between  the  jaws 
C  and  D,  as  it  is  an  easy  matter  by  springing  the  frame  of  the 
instrument,  or  compressing  the  rod,  to  change  the  reading  one 
or  more  of  the  smallest  units  given  by  it.  It  now  remains  to 
read  on  the  scale  the  length  of  the  rod.  On  C  will  be  seen  a 


THE  PROPERTIES   OF  MATTER.  1 

short  scale,  called  a  Vernier,  20  of  whose  divisions  equal  19  on 
the  bar  or  limb,  the  bar  divisions  being  fiftieths  of  an  inch. 
Hence,  each  division  of  the  vernier  is  y^^  of  an  inch  shorter 
than  each  bar  division.  Therefore,  write  down  the  number  of 
inches  and  fiftieths  of  an  inch  up  to  the  zero  of  the  vernier 
scale  ;  then  if  the  zero  of  the  vernier  does  not  register  exactly 
with  a  division  on  the  bar,  observe  which  one  of  the  vernier 
divisions  coincides  with  a  division  on  the  bar,  and  this  gives  the 
inimber  of  thousandths  to  be  added  to  the  quantities  already 
obtained.  Express  all  fractional  parts  decimally.  Make 
several  independent  measurements,  and  obtain  their  mean. 
Record  the  results  after  the  manner  described  in  previous 
exercises. 

The  index  on  the  opposite  side  of  this  instrument  is  ar- 
ranged for  both  inside  and  outside  measurements.  The  outer 
edges  of  the  jaws  are  rounded  for  insertion  in  tubes,  or  hollow 
cylinders  ;  then,  by  reading  from  the  index  marked  inside,  the 
distance  between  the  outer  surfaces  of  the  jaws  is  given,  that 
is,  the  diameter  of  the  tube. 

This  caliper  can  also  be  used  for  measuring  the  diameter 
of  a  cylinder,  the  diameter  of  a  small  ball,  or  the  thickness  of 
plates. 

7.  Exercise.  —  Determine  the  dimensions  of  a  piece  of 
brass  tubing.  Compute  the  lateral  surface  and  the  volume. 

The  best  instrument  for  this  purpose  is  the  Verniered 
Caliper.  Fair  results  can  be  got  by  the  direct  application  of 
a  good  scale. 

Enter  results  in  the  note-book  as  follows :  — 

Problem.  —  Determination  of  the  dimensions  of  a  piece  of  brass 
tubing.  Sept.  7,  1888. 

Method.  —  Verniered  caliper. 


8 


PRACTICAL   PHYSICS. 


Results.  — 

First  measurement . 
Second        " 
Third          " 


Length, 
in. 


Outside 
Diameter. 


Inside 
Diameter. 


Mean  .     .     . 
Computed  area  = 


.sq.  in. 


Volume  — 


8.  Exercise.  —  Cut  from  a  piece  of  wire  the  following 
lengths :  5  mm.,  1.26  inches,  2.39  inches,  149  mm.,  3.06  inches. 

With  a  pair  of  Cutting  Pliers  (Fig.  7),  or  a  file,  cut  off 
a  piece  of  wire  a  little  longer  than  is  required.  Set  the 


FIG.  7. 

verniered  caliper  to  the  required  length,  and  then,  with  a  fine 
file,  shorten  the  wire  till  it  fits  accurately  between  the  jaws. 
A  flat  scale  may  be  used  in  place  of  the  caliper  by  laying 
the  wire  directly  on  the  scale,  carefully  avoiding  parallax  in 
reading  by  always  sighting  across  the  ends  of  the  wire 
perpendicularly  to  the  scale. 

9.  Exercise.  —  Measure  the  diameter  of  a  wire,  and  also 
determine  the  gauge-number. 

The  diameter  can  be  found  by  means  of  the  verniered 
caliper  (Fig.  4),  but  a  better  instrument  for  the  purpose  is 
the  Micrometer  Caliper  (Fig.  8).  In  using  this  appliance,  it 
is  necessary  to  find  the  pitch  of  the  screw  C  by  observing 
the  graduation  of  the  linear  scale  a.  This  is  usually  either 


THE  PROPERTIES    OF  MATTER. 


9 


fiftieths  of  an  inch,  or  half -millimetres.  The  circular  scale  on 
D  is  generally  divided  into  20  parts  when  the  graduation  is  in 
English  measure,  and  25  when  French ;  so  that  a  circular 
division  represents  -fa  x  ^  =  y^^  °f  an  mcn  *n  the  one  case, 
and  ^  X  aV  =  A  °^  a  miUimetre  in  the  other.  As  these 
circular  divisions  are  large,  it  is  easy  to  estimate  to  quarters  of 
these  spaces.  When  the  screw  C  is  in  contact  with  B,  the 
zero  of  the  scale  on  D  should  be  at  the  zero  of  the  linear 
scale  a.  If  this  is  not  the  case,  the  set-screw  which  holds  B 
should  be  changed  till  the  zeroes  of  the  two  scales  coincide. 


Now  place  the  wire  to  be  measured  between  B  and  C.  and,  by 
turning  D,  advance  C  till  the  wire  is  held  between  B  and  C  ; 
being  careful  not  to  exert  undue  pressure,  as  it  is  an  easy 
matter  to  vary  the  reading  one  or  more  divisions  of  the  circular 
scale  by  springing  the  frame  of  the  instrument.  To  get  the 
reading,  observe  how  many  divisions  on  the  linear  scale  a  are 
exposed,  and  what  division  of  the  circular  scale  on  D  coincides 
with  the  line  running  lengthwise  of  the  cylinder  having  the 
linear  scale.  As  shown  in  Fig.  8,  we  have  the  following 
reading :  — 

On  the  linear  scale,  4  small  divisions  —  .08    inch. 
On  the  circular  scale,  5  divisions         =  .005  inch.    ' 


Total  reading 


=  .085  inch. 


10 


PRACTICAL   PHYSICS. 


When  the  linear  scale  is  graduated  to  read  to  fortieths  of  an 
inch,  the  larger  divisions  being  tenths,  then  the  circular  scale  is 
divided  into  25  parts,  and  hence  the  reading  is  to  thousandths. 

A  simple  method  of  measuring  the  diameter  of  a  wire  is  to 
wrap  it  closely  around  a  cylinder  whose  diameter  is  large  com- 
pared with  that  of  the  wire,  till  some  25  or  more  convolutions 
are  obtained.  Then  the  diameter  will  equal  the  width  of  the 
surface  covered  divided  by  the  number  of  turns. 

The  diameter  can  also  be  determined  by  weighing  accurately 
a  known  length  of  the  wire,  first  having  made  the  ends  square 


with  a  file.     Then  the  diameter  in  centimetres  = 


,  in 


which  w  =  weight  in  grammes,  d  =  density  (see  Table  II.), 

and  I  =  length  in 
centimetres.  For  an 
explanation  of  this 
formula,  consult  the 
subject  of  density  as 
presented  in  any  trea- 
tise on  Physics. 

To  ascertain  the 
gauge-number,  a  Wire- 
Gauge  (Fig.  9)  is  em- 
ployed. This  consists 
of  a  steel  plate  with 
a  graduated  series  of 
notches  around  the 
edge,  each  one  numbered  according  to  some  specified  table 
of  wire-gauges.  Find,  by  trial,  into  which  notch  the  wire 
will  just  fit,  and  read  off  the  number  on  the  gauge.  By 
reference  to  Table  VI.,  the  diameter  can  be  approximately 
found. 


FIG. 


THE  PROPERTIES    OF  MATTER. 


11 


10.  Exercise.  —  Measure  the  thickness   of   specimens  of 
the  following :  Paper,  mica,  tin-foil,  tinsel,  etc. 

The  most  suitable  instrument  for  this  problem  is  the  microm- 
eter caliper.  Make  several  measurements  of  each  specimen, 
and  devise  some  convenient  form  for  recording  the  results. 

11.  Exercise.  —  Measure  the  thickness  of  a  very  thin  piece 
of  mica. 

This  can  be  done  by  the  aid  of  the  micrometer  caliper ;  but 
a  more  desirable  instrument  for  making  such  measurements  is 
the  Spherometer  (Fig.  10),  as 
it  is  less  likely  to  break  the 
thin  plate,  and  the  moment 
of  contact  of  the  parts  of  the 
instrument  with  the  substance 
can  be  more  accurately  deter- 
mined, as  the  phenomenon  is 
independent  of  the  delicacy  of 
the  sensation  of  touch.  This 
instrument  consists  of  a  metal 
platform  supported  by  three 
steel  legs  whose  extremities  are 
the  vertices  of  an  equilateral  triangle.  In  the  middle  of  this  tri- 
angle is  a  fourth  leg,  which  can  be  raised  or  lowered  by  means  of 
a  fine  thread  cut  upon  it.  This  leg  passes  through  the  platform, 
and  terminates  above  in  a  finely  graduated  disk  of  such  a  size  as 
to  be  tangent  to  a  straight  scale  which  is  normal  to  the  plane  of 
the  triangle.  A  true  glass  plane  must  accompany  the  instru- 
ment. In  the  absence  of  any  thing  better,  a  piece  of  double- 
thick  French  plate  glass  may  be  used.  When  the  spherometer 
is  placed  on  the  plane  with  the  four  legs  touching  it,  the  zero 
on  the  disk  should  be  exactly  at  the  zero  of  the  straight  scale. 


Fro.  10. 


12  PRACTICAL   PHYSICS. 

If  found  not  to  be  in  adjustment,  loosen  the  screw  A,  and 
move  the  disk  the  necessary  amount.  In  reading  the  instru- 
ment, the  pitch  of  the  screw  must  be  known,  and  also  the 
number  of  divisions  on  the  disk.  Let  us  suppose  that  the  pitch 
is  ^  mm.,  and  that  the  disk  is  divided  into  500  parts  ;  then  one 
turn  of  the  disk  will  raise  or  depress  the  end  of  the  screw 
^  mm.,  and  to  turn  the  disk  through  one  division  of  its  scale 
will  move  the  screw  J  X  -g-Jo  =  -001  mm. 

To  measure  the  thickness  of  the  mica  plate,  place  the 
spherometer  on  the  glass  plane,  with  the  mica  under  the  fourth 
leg.  Turn  the  screw  till  the  instrument  starts  to  turn  on  the 
plate  from  the  friction  of  the  screw-leg  on  the  plate.  To 
the  reading  on  the  straight  scale,  add  that  on  the  disk,  and  the 
thickness  is  obtained.  Several  determinations  should  be  made, 
and  their  average  adopted  as  the  true  thickness,  making  a 
tabulated  record  of  the  work  as  directed  in  the  previous 
exercises. 

In  some  forms  of  the  instrument,  the  screw-leg  terminates 
below,  in  a  bent  lever  very  delicately  pivoted,  the  long  arm 
serving  as  a  pointer.  By  watching  the  pointer,  the  exact 
moment  of  contact  with  the  surface  is  known. 

Instead  of  adjusting  the  zero  of  the  instrument,  it  is  probably 
better  to  take  the  mean  of  several  readings,  when  standing  on 
the  plane,  without  the  mica,  and  then  subtract  this  from  the 
mean  of  as  many  readings  taken  with  the  mica  under  the  screw- 
leg.  Should  the  reading  in  the  first  case  be  below  zero,  and 
in  the  second  case  above,  the  two  must  be  added. 

12.  Exercise.  —  Measure  the  diameter  of  a  sphere,  as  a 
croquet-ball. 

First  Method.  —  Place  the  sphere  between  two  square-cut 
blocks  whose  faces  press  against  a  third  block,  and  measure 


THE  PROPERTIES   OF  MATTER.  13 

the  distance  between  the  first  two  by  means  of  a  good  scale. 
To  avoid  errors,  the  angles  of  the  blocks  must  be  square,  and 
the  thickness  of  the  blocks  must  not  be  less  than  half  the 
diameter  of  the  ball.  Why? 

Second  Method.  — Employ  the  Outside  Caliper  (Fig.  11)  and 
a  good  scale.  This  caliper  is  a  kind  of  compass  with  curved 
legs.  By  means  of  a  screw,  the  distance  between  the  inner 
faces  of  the  points  can  be  set  so  that  they  just  glide  over  the 


FIG.  11. 

surface  of  the  sphere.  Now  apply  the  points  to  the  scale  to 
determine  the  distance  between  them.  This  will  be  the  diameter 
of  the"ball.  Measure  the  ball  in  several  different  positions,  record 
the  results  as  in  previous  exercises,  and  obtain  the  mean. 

This  instrument  can  be  used  in  all  kinds  of  end  measure- 
ments where  actual  contact  between  the  instrument  and  the 
object  is  possible. 

13.  Exercise.  —  Measure  the  depth  and  also  the  diameter 
of  a  cylindrical  jar,  compute  its  contents,  and  compare  the 
result  with  that  obtained  by  the  use  of  a  graduated  measure. 
Employ  both  English  and  French  measure. 


14  PRACTICAL   PHYSICS. 

To  find  the  depth  of  the  jar,  stand  vertically  in  it  a  lineai 
scale,  taking  the  reading  on  it  at  the  point  opposite  the  lower 
edge  of  a  straight-edge  resting  across  the  top  of  the  jar.  This 
measurement  should  be  made  at  several  places,  as  the  bottom 
of  the  jar  is  not  perfectly  level.  The  inside  diameter  can  best 
be  found  by  means  of  the  Inside  Caliper  (Fig.  12).  Place 
the  instrument  within  the  jar,  and  open  it  as  far  as  possible. 
Apply  the  points  to  a  linear  scale,  and  find  the  distance 
between  their  outer  faces.  The  figure  shows  a  form  of  the 
caliper  that  can  be  used  for  both  inside  and  outside  measure- 
ments. 


FIG.  12. 


To  compute  the  volume,  apply  the  formula  V  —  vIPH,  in 
which  TT  =  3.1416,  R  =  radius,  and  H  =  depth. 

In  the  absence  of  an  inside  caliper  bend  a  piece  of  annealed 
wire  into  a  U-shape,  and  use  it  in  the  same  way  as  a  caliper. 
The  lack  of  elasticity  will  cause  the  points  to  stay  wherever 
placed. 

To  measure  the  volume  of  the  jar,  ascertain  how  much  water 
it  takes  to  fill  it,  as  measured  both  in  and  out  with  a  Graduate 
(Fig.  254.)  In  filling  the  graduate,  place  it  on  a  horizontal 
table,  and  in  taking  the  reading  hold  the  eye  on  a  level  with 
the  surface  of  the  water. 

A  simple  method  of  finding  the  volume  of  small  vessels  of 
any  shape  is  to  subtract  their  weight  when  empty  from  that 
when  filled  with  ice- water.  This  difference,  in  grammes,  will, 
be  the  volume  in  cubic  centimetres. 


THE  PROPERTIES   OF  MATTER.  15 

Record  the  results  after  some  such  plan  as  the  following :  — 

Problem.  —  Determination   of    the   contents   of    a   cylindrical    jar. 
Sept.  7,  1888. 

Method.  —  Linear  scale,  inside  caliper,  water,  and  a  graduate. 

Results.  — 

Depth.  Diameter.  Capacity. 

First  measurement .  cm. in.     cm. in.     ccm.  oz. 

Second         " 
Third 


0 
Mean  .... 


Computed  volume   .  ccm.  oz. 

Measured        " 

Mean  ....  

14.  Exercise.  —  Copy  a  scale  on  glass,  brass,  or  paper. 

Thoroughly  clean  the  piece  of  glass  or  brass,  and  coat  it 
evenly  with  a  thin  film  of  beeswax  or  paraffin e  by  plunging 
it  into  a  dish  filled  with  the  melted  substance.  Fasten  both  the 


FIG.  13. 

scale  to  be  copied  and  the  piece  of  brass  or  glass  to  a  board  by 
means  of  tacks  so  as  to  be  about  50  cm.  apart.  In  a  wooden 
bar  about  52  cm.  long,  2  cm.  wide,  and  1  cm.  thick,  insert  at 
each  end,  and  perpendicular  to  the  length,  a  stout  needle-point 
2  cm.  long  (Fig.  13).  Place  one  of  the  needle-points  of  the 
bar  on  the  first  division  of  the  scale,  and  with  the  other  point 
draw  a  line  in  the  wax  cutting  entirely  through  it.  Next  place 


16  PRACTICAL   PHYSICS. 

the  needle-point  on  the  second  division  of  the  scale,  and  so  on 
till  a  scale  of  sufficient  length  has  been  obtained.  Every  fifth 
division  should  be  made  a  little  longer  than  the  others,  and 
every  tenth  should  be  longer  still.  With  a  sharp-pointed 
instrument  add  the  proper  figures.  If  the  scale  is  on  brass, 
flow  the  plate  with  nitric  acid  for  a  few  moments,  and  then 
wash  in  water.  If  the  scale  is  on  glass,  place  the  plate,  writing 
downward,  over  a  rectangular  dish  made  of  sheet-lead,  and 
containing  a  spoonful  of  powdered  fluor-spar  well  moistened 
with  sulphuric  acid.  Warm  the  vessel  slightly  over  a  lamp, 
being  careful  not  to  melt  the  wax,  and  set  aside  for  a  few  hours. 
Remove  the  wax  with  a  cloth  wet  with  benzine.  A  scale  will 
be  found  etched  in  the  glass  or  brass,  as  the  case  may  be. 

To  copy  a  scale  on  paper,  substitute  for  one  of  the  needles 
on  the  bar  a  draughtsman's  right-line  pen  or  a  hard  lead- 
pencil,  inserting  it  in  a  hole  bored  through  one  end  of  the  bar. 

15.  Exercise.  —  Test  the  accuracy  of  the  divisions  of  a 
common  linear  scale. 

To  obtain  the  deviation  from  a  standard  scale,  employ  the 
Beam-Compass  (Fig.  14).  It  consists  of  a  graduated  bar  of 
wood  or  metal,  the  standard  scale,  to  which  are  attached  by 
clamps  two  points,  one  of  which  has  a  fine  adjustment  by 
means  of  a  tangent-screw,  C,  causing  the  index-mark  on  B 
to  move  in  front  of  a  fine  scale.  The  instrument  may  also 
be  used  in  measuring  distances  between  points,  in  copying 
scales,  etc. 

Fasten  the  scale  to  be  tested  to  a  board.  Slide  the  point  A 
along  the  bar  till  the  distance  between  A  and  B  is,  roughly, 
equal  to  the  distance  on  the  scale  to  be  tested.  Then  clamp  A, 
place  the  point  on  the  scale,  and  move  B,  by  means  of  C,  till 
the  points  fall  exactly  on  the  scale  divisions.  Use  a  magni- 


THE  PROPERTIES  OF  MATTER. 


17 


fying-glass  to  insure  accuracy  in  the  coincidence  of  the  points 
with  the  divisions  of  the  scale.  Now  read  the  distance  on  the 
beam,  and  combine  it  with  the  reading  on  C,  for  the  distance 
between  the  scale  divisions.  Proceed  in  this  way  till  as  much 
of  the  scale  as  needed  has  been  tested. 


The  results  may  be  recorded  as  follows  :  — 

Problem.  —  Testing  the  accuracy  of  a  linear  scale.    Sept.  8, 1888. 
Method.  —  The  beam-compass. 
Results.  — 
Scale  Reading.         Compass-Bar  Reading.      Scale  C  Reading.  True  Distance. 


16.  Exercise.  —  Divide  a  straight  line  into  a  number  of 
equal  parts. 

First  Method.  —  Through  one  end  of  the  line  to  be  divided, 
draw  an  indefinite  straight  line  making  any  angle  between  30° 
and  45°.  Lay  off  on  this  line  with  the  dividers  as  many 
equal  distances  as  there  are  parts  required  of  the  given  line, 


18  PRACTICAL  PHYSICS. 

beginning  at  the  vertex  of  the  angle.  Join  the  last  division 
with  the  free  end  of  the  given  line,  and  through  the  other  points 
of  division  draw  lines  parallel  to  this  line.  This  set  of  parallels 
will  divide  the  line  as  required. 

To  draw  parallel  lines,  place  one  side  of  a  wooden  triangle, 
such  as  draughtsmen  use,  firmly  against  the  edge  of  a  ruler  rest- 
ing on  the  paper.     Then  on  sliding  the  triangle  along  the  ruler, 
either  of  the  other  sides  will  move  parallel  to  its  first  position. 
/Second  Method.  —  Employ  a  pair  of  Proportional  Dividers 
(Fig.  15).     This  instrument  is  a  variety  of   a 
double  compass  with  a  movable   axis,   a  scale 
&u  the  side  indicating  the  ratio  of  the  distance 
between  one  pair  of  points  to  that  between  the 
other  pair  as  the  compass  is  opened.     It  is  some- 
times furnished  with  a  micrometer  adjustment. 
The  same  instrument  is  also  graduated  so  as  to 
give    the    length   of    the   side    of    any   regular 
polygon  for  any  given  radius. 

To  divide  the  given  line,  set  the  index  at  that 
division  on  the  scale  of  the  instrument  indicating 
the  required  number  of  parts  into  which  the  line 
is  to  be  divided.  Now  open  the  dividers  till  the 
distance  between  the  points  of  the  longer  legs  is 
the  length  of  the  line  ;  then  the  distance  between 
the  other  two  points  is  the  required  part  of  the 
line.  Lay  this  distance  off  on  the  line,  and  the 
required  division  is  obtained. 
FIG.  15.  By  reversing  the  process,  a  line  may  be  ex- 

tended to  any  number  of  times  its  original  length. 

17.  Exercise.  —  Draw  a  circle  on  cardboard,  and  divide  it 
into  degrees. 


THE  PROPERTIES   OF  MATTER.  19 

This  will  require  the  use  of  a  Protractor  (Fig.  16),  a  brass, 
German- silver,  or  translucent  horn  circle  or  semicircle  divided 
to  degrees  or  half  degrees.  It  is  frequently  provided  with  an 
arm  turning  about  its  centre,  and  so  constructed  that  one  edge 
of  it  moves  exactly  as  a  radius  of  the  circle.  For  very  accu- 
rate work  the  readings  are  made  by  means  of  a  vernier.  When 
not  provided  with  an  arm,  a  ruler  will  have  to  be  used  instead. 


FIG.  16. 

Place  the  protractor  on  the  cardboard  circle  so  that  the  cen- 
tres coincide.  Then  set  the  radial  arm  at  zero,  and  with  a 
sharp  pencil  draw  a  line  along  the  edge  cutting  the  circumfer- 
ence of  the  circle.  Now  move  the  arm  to  the  successive 
divisions  of  the  scale,  and  mark  as  before.  Make  every  fifth 
division  line  longer  than  the  others,  and  every  tenth  longer 
still.  Should  the  circle  be  smaller  than  the  protractor,  rule  the 
radial  lines  as  before ;  then  remove  the  instrument,  and  by  the 
aid  of  a  ruler  extend  the  lines  toward  the  centre  till  they 
intersect  the  circumference. 

18.  Exercise.  —  Draw  a  triangle  on  a  piece  of  cardboard, 
measure  its  angles  and  sides,  and  also  compute  its  area. 

The  length  of  the  sides  can  be  obtained  by  the  method  of 
Art.  2.  To  measure  an  angle,  place  the  protractor  so  that  its 


20  PRACTICAL   PHYSICS. 

centre  is  exactly  on  the  vertex,  and  the  zero  is  in  one  side  of 
the  angle,  or  that  side  produced.     Now  move  the  arm  till  it  is 
iii  the  other  side  ;  the  reading  will  be  the  value  of  the  angle. 
The   area   can   be    computed    by   the  aid    of    the    formula 


~~  a)  (P  ~~  fy(P  ~  c)->  m  which  p  is  the  semi-perimeter, 
and  a,  6,  and  c  are  the  sides.  An  approximation  to  the  area 
of  the  triangle,  and  in  fact  of  any  plane  figure,  can  be  obtained 
by  transferring  it  to  what  is  known  as  cross-section  paper, 
paper  divided  accurately  into  small  squares  of  known  size,  and 
counting  the  number  of  these  squares  that  the  figure  includes. 
Wherever  but  part  of  a  square  falls  within  the  triangle,  the 
value  of  that  part  will  have  to  be  carefully  estimated. 

Another  simple  method  is  to  cut  the  figure  out  of  cardboard, 
and  compare  its  weight  with  that  of  a  square  inch  or  a  square 
centimetre  cut  from  the  same  cardboard. 

19.  Exercise.  —  Draw   on    paper   a   figure   bounded   by 
several  straight  lines,  and  determine  its  area. 

Divide  the  figure  into  triangles,  and  compute  their  areas  as 
in  Art.  18.  Check  the  work  by  applying  the  approximative 
methods  suggested  in  the  same  article. 

20.  Exercise.  —  Find  the  volume  of  any  irregular  piece  of 
stone  or  metal. 

First  Method.  —  Measure  the  volume  of  water  the  substance 
displaces.  To  do  this  readily  and  accurately,  a  Cylindrical 
Graduate  (Fig.  254)  and  an  Erdmann's  Float  (Fig.  17)  are 
needed.  The  float  is  a  short  glass  cylinder,  closed  at  both  ends, 
and  weighted  with  mercury  so  as  to  cause  it  to  take  an  upright 
position  in  the  water.  A  mark  is  etched  around  the  cylinder,  and 
the  position  of  this  mark  with  reference  to  the  scale  on  the 
graduate  is  the  reading  to  be  used.  To  make  a  float,  select  a 


THE  PROPERTIES  OF  MATTER.         21 

short  piece  of  thin  glass  tubing,  close  one  end  by  heating  it  in 
a  gas-flame,  then  introduce  mercury  or  shot  sufficient  to  cause 
the  tube  to  float  in  a  vertical  position  in  water.  Now  close  the 
other  end  of  the  tube  by  softening  the  glass  and  draw- 
ing it  out  to  form  a  hook.  A  fine  thread  tied  around 
the  tube  at  a  point  which  will  be  below  the  surface 
when  the  instrument  floats  in  water  will  serve  as  an 
index.  The  office  of  the  float  is  to  avoid  the  error  due 
to  the  liquid's  climbing  up  the  side  of  the  cylinder, 
rendering  it  difficult  to  tell  where  the  upper  surface  is. 
Fill  the  graduate  part  full  of  water,  introduce  the 
float  by  means  of  a  wire  hook,  and  observe  the  position  FlG  17 
of  the  line  on  the  float  with  reference  to  the  scale  on 
the  graduate.  By  introducing  water  drop  by  drop,  this  reading 
can  always  be  made  a  whole  number.  In  taking  readings, 
always  read  to  that  division  on  the  scale  that  is  in  line  with  two 
opposite  points  of  the  line  around  the  float.  Now  remove  the 
float,  and  introduce  the  object  to  be  measured ;  then  replace 
the  float,  and  take  the  readings  as  before.  The  difference 
between  the  two  readings  is  the  volume.  Make  several 
measurements,  varying  the  quantity  of  water,  and  record  the 
results  after  some  such  plan  as  the  following :  — 

Problem.  —  Determination  of  the  volume  of  an  irregular  piece  of 
stone.    Sept.  10,  1888. 

Method.  —  Water,  Erdmann's  float,  and  graduated  cylinder. 

Results.  — 

Float-reading  before  introducing    Float-reading  after  introducing 
the  Stone.  the  Stone. 

First  observation     .  ccm.  ccm. 

Second         "  .    „ 

Third  " 


Mean 

Volume.    .....*..  ccm. 


22  PRACTICAL   PHYSICS. 

Second  Method. — The  volume  of  a  substance  whose  density 
is  known  can  be  found  in  cubic  centimetres  by  dividing  its 
weight  in  grammes  by  the  density.  Consult  Art.  187  and 
Table  II. 

21.  Exercise.  —  Find  the  volume  of  a  substance  soluble  in 
water,  as  rock-candy,  common  salt,  etc. 

Sugar  and  saltpetre  are  insoluble  in  strong  alcohol ;  common 
salt  in  sulphuric  ether,  etc. 

22.  Exercise.  —  Find  the  capacity  of  a  vessel  whose  form 
is  that  of  the  frustum  of  a  cone. 

If   the  vessel  is   a   small   one   its    capacity  can   be   readily 
obtained  by  means  of  a  graduated  measure.     If,  however,  the 
vessel  is  large,  like  a  water-pail,  its  capacity  is  easily  com- 
puted by  the  formula  —  (R2  +  r2  +  Rr),  in  which  TT  =  3.1416, 
3 

H  =  depth,  R  =  radius  of   the  top,  and   r  =  radius   of  the 
bottom.     These  dimensions  are  found  as  directed  in  Art.  13. 
Record  the  results  as  follows  :  — 

Problem.  —  Determination  of  the  capacity  of  a  vessel  whose  form  is 
that  of  the  frustum  of  a  cone.     Sept.  10,  1888. 
Method.  —  By  calipers  and  scale. 
Results.  — 

Diameter  of       Diameter  of 

Top.  Bottom.  Depth. 

First  measurement    .    .    cm.    cm.     .cm. 

Second         "  .     .    

Third 


Mean _ „. 

Volume ccm. 


THE  PROPERTIES   Of  MATTER.  23 

II.     ESTIMATION    OF   MASS. 

23.  Apparatus.  —  As  the  mass  of  a  substance  —  that  is,  the 
quantity  of  matter  in  it  —  is  estimated  in  terms  of  some  quantity 
of  matter  assumed  as  a  standard,  as  the  gramme  or  avoirdupois 
pound,  there  is  therefore  needed  for  its  determination  a  copy 
of  the  standard  unit,  together  with  multiples  and  sub-multiples, 
as  well  as  some  form  of  balance  for  making  the  comparison. 


FIG.  18. 

The  Balance  (Fig.  18)  consists  of  a  metal  beam  supported 
on  an  axis  perpendicular  to  its  length,  and  about  which  it  is 
free  to  turn  in  a  vertical  plane.  Pans  are  attached  at  the 
extremities  of  the  beam  in  such  a  manner  as  to  move  freely 
about  an  axis  parallel  to  the  axis  supporting  the  beam.  All 
the  bearings  are  usually  knife-edges  of  hardened  steel  resting 
on  polished  agate  or  steel  plates.  Attached  to  the  centre  of 
the  beam  is  a  long  pointer  moving  in  front  of  a  graduated 
scale,  to  tell  the  user  when  the  beam  is  horizontal.  In  order 


24 


PRACTICAL  PHYSICS. 


that  the  beam  may  not  rest  on  the  bearings  when  the  balance  is 
not  in  use,  a  provision  is  made,  such  that  by  turning  a  mill- 
head  in  front,  the  beam  is  lifted  from  its  supports.  To  protect 
from  air-currents  when  weighing,  a  glass  case  covers  the 

balance.  This  case  is  sup- 
ported on  levelling-screws  to 
facilitate  the  adjustment  of 
the  instrument  to  that  posi- 
tion in  which  the  pointer  is 
opposite  the  middle  division 
of  the  scale.  Fig.  19  illus- 
trates a  cheaper  form  of 
FIG.  19.  balance,  which  will  be  found 

sufficiently  accurate  for  all  requirements  of  this  book.  In  fact, 
the  common  hand-balance  so  largely  used  by  jewellers,  if 
suspended  from  some  simple  support,  will  give,  with  care  and 
patience,  very  good  results. 

Jolly's  Balance  (Fig.  20)  is  a  cheap  and  efficient  substitute 
for  the  beam  balance.  To  construct  one,  proceed  as  follows  :  — 
Provide  a  stout  supporting-rod  set  into  a  square  block  for 
a  base.  Suspend,  from  an  arm  projecting  from  the  top,  a 
delicate  spiral  spring  30  cm.  long.  Two  or  three  of  these 
springs  should  be  provided,  varying  in  stiffness.  They  are 
made  by  winding  spring  brass  wire  closely  around  a  cylinder 
2  cm.  in  diameter.  Wires  ranging  from  No.  20  to  No.  30  may 
be  used,  according  to  the  sensitiveness  required.  Attach 
two  small  scale-pans  as  seen  in  the  figure,  the  lower  to  be 
used  in  density  determinations  for  weighing  objects  in  water, 
an  adjustable  shelf  being  necessary  to  support  the  tumbler. 
On  the  standard  back  of  the  spring,  tack  a  long  strip  of  mirror 
on  which  is  a  millimetre  scale  (see  Art.  14).  Instead  of  etching 
the  scale  on  the  face  of  the  mirror,  it  will  be  simpler  to  cut  it 


THE  PROPERTIES   OF  MATTER. 


25 


in  the  amalgam,  and  then  cover  the  back  with  black  paper.  A 
paper  scale  cemented  along  the  edge  of  the  mirror  will  answer 
nearly  as  well.  Just  above  the  scale-pan,  attach  a  small  white 
bead,  or  a  wire  pointer,  at  right  angles  to 
the  spring,  to  serve  as  an  index.  The 
scale-reading  is  where  the  line  joining 
the  index  with  its  reflection  intersects  the 
scale. 

The  Weights  (Fig.  21),  when  large, 
are  made  of  brass  ;  when  small,  of  either 
aluminum  or  platinum.  Each  weight  has 
its  value  stamped  upon  it,  and  should 
have  its  assigned  place  in  a  neat  box. 
In  handling  them,  always  use  the  small 
pair  of  pincers  found  in  the  case.  The 
milligramme  weights  are  not  much  used 
where  the  balance-beam  is  graduated. 
Their  place  is  supplied  by  what  is  known 
as  the  Rider,  a  U-shaped  piece  of  wire, 
usually  weighing  one  centigramme,  that  is 
placed  astride  of  the  beam.  If  the  arms, 
for  example,  are  each  divided  into  ten 

parts,      then     the 

rider     placed      at 

division  six  repre- 

sents  a  weight  of 

six  -  tenths     of     a 

FlG- 21-  centigramme,  or  6 

milligrammes,  placed  on  the  scale-pan.  By  estimating  fractions 
of  these  divisions,  or  using  lighter  riders,  fractions  of  milli- 
grammes can  be  weighed. 


FIG.  20. 


26 


PRACTICAL  PHYSICS. 


24.  Exercise.  —  Find  the  weight  of  a  small  piece  of  any 
substance. 

Set  the  balance  vibrating,  with  empty  pans,  to  determine 
the  position  of  the  resting-point  of  the  pointer  on  the  ivory 
scale.  Since  it  will  take  too  much  time  to  allow  the  beam  to 
come  to  rest,  it  is  better  to  determine  where  the  resting-point 
would  be  by  observations  made  on  the  oscillations.  This  would 
be  an  easy  matter  if  the  resting-point  was  the  middle  point  of 
the  arc  described  by  the  pointer.  But  the  distance  the  pointer 
swings  each  side  of  the  resting-point  gradually  diminishes  ; 
hence  it  will  be  necessary  to  average  a  number  of  oscillations 
after  the  manner  described  below. 

Suppose  the  ivory  scale  to  be  divided  into  thirty  parts.  To 
avoid  the  use  of  signs  in  distinguishing  the  deviations  of  the 
pointer  to  the  right  or  left  of  the  middle  division,  number 
the  scale  from  left  to  right,  the  extreme  left  being  marked  0, 
the  middle  15,  and  the  extreme  right  30.  Then  record  five 
vibrations  of  the  pointer.  This  will  give  the  greatest  and 
the  least  arc  to  the  side  toward  which  the  pointer  was  first 
observed  to  move.  These  would  be  recorded  as  follows  :  — 


TURNING-POINTS. 

RESTING-POINT. 

Left. 

Right. 

First  vibration, 
Third        " 
Fifth         " 

Mean    .    . 

3 
5.3 

7 

Second  vibration, 
Fourth        " 

Mean  .     .     . 

25 
22.2 

5.1  +  23.6 

Mean  —  -                 —  14.  oo. 

a 

5.1 

23.6 

Hence  14.35  is  the  resting-point  of   the  unloaded  balance. 
By  means  of  the  le veiling-screws,  the  balance  could  be  adjusted 


THE  PROPERTIES   OF  MATTER.  27 

so  that  the  resting-point  would  be  the  middle  division  of  the 
scale,  but  it  is  unnecessary.  Now  place  the  article  to  be 
weighed  on  the  left-hand  scale-pan,  and  as  near  the  middle  as 
practicable.  In  the  other  pan,  place  a  weight  such  as  you 
estimate  will  balance  it.  Now  throw  the  balance  in  action, 
and  watch  the  pointer  to  determine  which  pan  is  the  heavier, 
since,  if  the  equilibrium  is  not  close,  the  pointer  will  move 
sharply  to  one  side  of  the  resting-point,  whereas,  if  close,  the 
resting-point  will  be  seen  to  be  near  the  middle  of  the  arc 
described.  If  the  weight  is  found  too  heavy,  remove  it,  and 
substitute  a  smaller  one  ;  if  too  small,  a  heavier  one.  Let  us 
suppose  that  the  twenty-gramme  weight  is  found  too  heavy. 
Then  replace  it  by  the  ten-gramme  weight.  If  this  is  found 
too  light,  then  add  the  five-gramme  weight ;  if  still  too  light, 
add  two  more  ;  if  now  too  heavy,  then  replace  the  two-gramme 
by  the  one-gramme  ;  if  now  too  light,  add  .5  gramme  ;  if  still 
too  light,  add  .2  gramme  ;  if  now  too  heavy,  replace  .2  gramme 
by  .1  gramme,  and  so  on.  When  traced  down  to  centigrammes, 
the  centigramme  rider  may  be  used  if  the  balance  has  a 
graduated  beam,  and  the  milligrammes  determined. 

When  the  swinging  of  the  pointer  shows  that  the  balance  is 
nearly  secured,  find  the  resting-point  of  the  loaded  balance  in 
the  same  manner  as  in  the  case  of  the  unloaded.  Let  us 
suppose  that  is  found  to  be  13.5.  This  shows  that  the  right- 
hand  pan  is  the  heavier.1  To  determine  the  amount,  place 
.001  gramme  in  the  left-hand  pan,  and  again  determine  the 
resting-point.  Let  us  suppose  that  this  resting-point  is  found 
to  be  15.  Hence  it  follows  that  .001  gramme  has  moved  the 
pointer  through  15  —  13.5  =  1.5  divisions,  whereas  it  was 


1  This  applies  to  a  balance  having  the  ivory  scale  below  the  beam.    Where  this  scale 
is  above  the  beam,  the  opposite  is  indicated. 


28  PRACTICAL  PHYSICS. 

necessary  to  move  it  14.35  —  13.5  =  .85  division.  Therefore 
the  amount  to  be  placed  in  the  left-hand  pan,  that  is,  the 
amount  to  be  deducted  from  the  weights  in  the  right-hand  pan, 
is  (.85  -r-  1.5)  x  .001  =  .00057  gramme.  Finally  add  together 
the  weights  in  the  pan,  and  deduct  from  the  sum  .00057  gramme 
to  obtain  the  weight  of  the  substance. 

To  prevent  errors  in  determining  the  total  value  of  the 
weights  on  the  pan,  first,  add  up  the  values  of  those  which 
the  empty  pockets  of  the  case  show  to  be  in  use ;  secondly, 
check  the  same  by  adding  the  values  of  the  weights  as  they  are 
removed  from  the  pan  to  the  case. 

In  weighing  with  fine  balances,  observe  the  following  precau- 
tions :  — 

1.  Remove  all  dust  from  the  pans  by  means  of  a  camel-hair 
brush. 

2.  Set  the  balance  in  action  by  turning  the  mill-head  to  find 
the  resting-point  of  the  pointer,  as  it  is  not  always  the  middle 
division  of  the  scale. 

3.  When  it  is  necessary  to  stop  the  swinging  of  the  beam, 
wait  till  the  pointer  is  directly  over  the  centre  of  the  scale,  then 
turn  the  mill-head.     To  do  otherwise  jars  the  instrument,  and 
injures  the  bearings. 

4.  Always  stop  the  swinging  of  the  balance  when  adding  or 
removing  weights. 

5.  The  position  of  the  observer  should  be  central  so  as  to 
avoid  any  parallax  in  reading  the  scale. 

6.  Always  put  on  weights  in  the  order  in  which  they  come 
in  the  box  or  case,  handling  them  with  the  pincers,  and  never 
with  the  fingers. 

7.  When  the  weighing  is  finished,  replace  the  weights  in  the 
box,  and  in  no  case  leave  the  balance  swinging  if  there  is  any 
provision  for  avoiding  it. 


THE  PROPERTIES   OF  MATTER.  29 

8.  Avoid  all  air-currents,  and  have  a  firm  support  for  the 
balance,   so  that   there   may  be  as  little  trembling  as  possi- 
ble. 

9.  Never    be    in   a   hurry,    as    accurate   weighing    is    slow 
work. 

10.  All  substances  liable  to  injure  the  pans,  when  being 
weighed,  must  be  placed  in  appropriate  vessels  ;  a  watch-glass 
of   known   weight   will   be   found  very  useful   for   such   pur- 
poses. 

To  weigh  with  Jolly's  balance,  place  the  substance  in  the 
upper  pan,  and  take  the  reading  of  the  index.  Now  remove 
the  substance,  and  add  weights  till  the  same  reading  is 
obtained.  The  sum  of  the  weights  is  evidently  the  weight  of 
the  substance.  If,  with  the  weights  given,  it  is  found 
impossible  to  bring  the  index  to  the  same  reading,  add  weights 
till  a  reading  less  than  the  required  one  is  obtained,  but  such 
that  the  smallest  weight  on  hand,  when  added,  brings  the  index 
too  low.  If,  for  example,  the  reading  required  is  300,  and 
1  mg.  changes  it  from  299  to  301.5,  then  the  weight  required 

will  be  —  of  1  mg.,  or  .4  mg. 

2i.D 

25.  Exercise.  —  Determine  the  weight  of  a  number  of 
lead  balls  by  weighing  five  of  them  separately,  selected  at 
random,  finding  their  average,  and  multiplying  that  average 
by  the  number  of  balls  in  the  lot.  Weigh  each  ball  several 
times. 

The  record  may  have  the  following  form :  — 

Problem.  —  Determination  of  the  weight  of  a  number  of  lead  balls. 

Method.  —  Weighing  five  of  them  separately,  selected  at  random, 
finding  their  average,  and  multiplying  that  average  by  the  number  of 
balls  in  the  lot. 


30  PRACTICAL  PHYSICS. 

Results.  — 

First  Ball.      Second  Ball.    Third  Ball.    Fourth  Ball.     Fifth  Ball. 

First  weighing    .  

Second      "         . 

Third        " 


Mean  .     .     . 
Average  weight  of  a  ball  = Weight  of  lot  = 

26.  Exercise.  —  Determine  how  many  grains  of  wheat  in  a 
bushel,  60  pounds,  by  weighing  five  lots  of  20  grains  each,  and 
from  these  data  determining  the  average  weight  of  a  grain. 

Devise  a  convenient  form  for  recording  the  results. 

27.  Exercise.  —  Determine  how  much  chalk  it  takes  to 
write  your  name  on  a  common  blackboard.      Also  determine 
the  amount  used  in  writing  your  name  on  a  slate.    Which  is  the 
more  economical  surface  on  which  to  use  chalk  ? 

Use  the  mean  of  several  times'  writing.  Devise  some 
suitable  form  for  tabulating  results. 

28.  Exercise.  —  Determine  the  weight  of  a  silver  five-cent 
piece,  and  also  that  of  a  silver  dollar.     What  is  the  value  of 
the  silver  dollar  on  the  standard  adopted  for  the  five- cent  piece  ? 

29.  Exercise.  —  Determine  the   percentage   of    water  in 
crystallized  sodium  sulphate. 

Weigh  carefully  a  large  crystal  of  the  salt,  and  then  set  it 
aside  for  several  days  in  a  place  where  dust  is  excluded. 
The  crystal  will  fall  to  powder,  owing  to  the  escape  of  the 
water  of  crystallization.  Find  the  weight  of  the  powder,  and 
then  compute  the  percentage  of  loss. 


THE  PROPERTIES   OF  MATTER.  31 

30.  Exercise.  —  Compare  the  weights  of  equal  volumes  of 
several  substances,  expressing  each  in  terms  of   the  lightest 
taken  as  the  unit. 

Get  a  competent  mechanic  to  make  out  of  lead,  brass,  tin, 
iron,  maple,  lignum-vitse,  etc.,  cubical  blocks  1.5  cm.  on  an 
edge,  that  is,  blocks  of  equal  volumes,  and  determine  their 
weights  in  the  regular  way. 

31.  Exercise.  —  Determine  the  length  of  a  twisted  piece  of 
wire. 

Weigh  several  straight  pieces  of  wire  of  the  same  material 
and  gauge-number,  and  also  measure  their  lengths.  From 
these  data,  compute  the  average  weight  of  a  centimetre  of  the 
wire.  Now  weigh  the  twisted  piece,  and  compute  its  length. 

The  results  may  be  recorded  as  follows  :  — 

Problem.  —  Determination  of  the  length  of  a  twisted  piece  of  wire. 
Method.  —  Weighing  and  measuring. 

Results.  — 

Length.  Weight.         Weight  per  Centimetre. 

Wire  No.  1     .     .    

"      "    2 


Mean 

Weight  of  the  twisted  piece, Computed  length,  

32.  Exercise.  —  Cut  a  piece  of  smooth  tin-foil  of  some 
simple  figure  ;  determine  its  area  and  weight.  Compute  its 
thickness,  allowing  that  1  ccm.  of  tin  weighs  7.29  grammes. 
Compare  the  result  with  that  obtained  by  the  use  of  the 
micrometer  caliper.  Devise  a  suitable  form  of  record  in  the 
note-book. 


32  PRACTICAL  PHYSICS. 

33.  Exercise.  —  Make  out  of  aluminum-foil  a  centigramme 
weight. 

First  find  both  the  area  and  the  weight  of  a  piece  of  the 
foil,  and  then  compute  how  large  a  piece  will  be  required  to 
weigh  one  centigramme.  As  the  thickness  of  the  metal  may 
not  be  uniform,  cut  the  piece  a  trifle  larger  than  the  estimated 
one.  By  means  of  a  fine  file,  adjust  the  piece  to  the  required 
weight. 

34.  Exercise.  —  Measure  the  cross-section  of  a  capillary 
glass  tube. 

Clean  the  tube  thoroughly  by  washing  it,  first  in  nitric  acid, 
then  in  distilled  water,  then  in  a  solution  of  sodium  hydrate, 
and  finally  in  distilled  water.  To  do  this,  connect  a  small 
glass  syringe  to  the  tube  to  be  washed,  by  half  a  metre  of 
rubber  tubing  ;  then,  by  placing  one  end  of  the  capillary  tube 
in  a  vessel  containing  the  wash,  the  corrosive  liquid  is  made  to 
pass  backward  and  forward  through  the  tube  without  coming 
in  contact  with  the  hand.  After  thoroughly  washing  the  tube 
with  distilled  water,  rinse  it  out  with  alcohol,  and  then  dry  it 
by  passing  it  back  and  forth  over  a  gas  or  spirit  flame.  Fill 
the  tube  part  full  of  pure  mercury  by  dipping  it  into  a  dish 
filled  with  the  liquid ;  lay  it  on  a  horizontal  surface  and  by 
means  of  a  pair  of  dividers  and  a  diagonal  scale,  ascertain 
the  length  of  the  mercury  filament.  Pour  the  mercury  out 
of  the  tube  into  a  suitable  vessel  of  known  weight,  and  ascer- 
tain its  weight.  Now  the  volume  of  mercury  in  the  tube  is 
equal  to  the  weight  of  mercury  divided  by  13.6,  and  the  cross- 
section  of  the  tube  equals  the  volume  of  mercury  divided 
by  the  length  of  the  filament,  provided  the  centimetre  and 
the  gramme  are  the  units  used.  How  would  you  find  the 
diameter  ? 


THE  PROPERTIES   OF  MATTER.  33 


III.     IMPENETRABILITY. 

35.  Apparatus.  —  The  principal  appliances  needed  in  the 
study  of  this   subject  are   as   follows :    Battery -Jar,  Cubes  of 
"Wood,  Funnel,  Funnel-Tube  with   a   Stop-Cock,  Rectangular 
Prism  of  Wood,  Wide-Mouthed  Bottle,  Tumbler,  Glass  Tubing 
and  a  Cylindrical  Graduate. 

36.  Exercise.  —  Graduate   a   glass  battery-jar  of  two  or 
more  litres  capacity  to  decilitres   by  means  of   a   graduated 
measure  and  water,  marking  the  divisions  on  a  paper  strip 
pasted   on   the   outside.      Cut   out   of   wood  two   cubes,   one 
decimetre  and  one-half  a  decimetre  on  their  edges  respectively. 
Give   each   block   a   coat   of   thin   shellac   varnish,    made    by 
dissolving  shellac  in  alcohol,  or  of  hot  paraffine.     Now  fill  the 
jar  about  half   full   of   water,   and  observe  by  the  scale  on 
the  side  exactly  how  much  there  is.      Then  place  in  the  jar 
these  blocks  successively,  holding  the  block  under  water  by 
means  of  a  slender  knitting-needle,  and,  while  submerged,  note 
exactly  the  volume  of  water  as  shown  by  the  scale  on  the  side 
of  the  jar.    Compare  the  increase  of  volume  with  the  volume  of 
the  block.     Inference. 

Owing  to  the  climbing-up  of  the  water  on  the  side  of  the  jar, 
it  is  difficult  to  get  the  exact  position  of  the  surface.  This 
may  be  partly  corrected  by  rubbing  a  thin  film  of  paraffine  on 
the  inside  of  the  jar  opposite  the  scale. 

37.  Exercise.  —  Partly  close  the  throat  of  a  funnel  with  a 
perforated  cork.      Fit   a   second   cork  accurately  to   a   wide- 
mouthed  bottle  with  the  stem  of   the  funnel  passing  tightly 
through  this  cork  (Fig.  22).     Bore  a  small  hole  through  this 
cork  of   about  2  mm.  diameter.      Now  pour  water  into   the 


34 


PRACTICAL  PHYSICS. 


funnel,  holding  a  finger  firmly  over  this  small  hole  in  the  cork. 
Observe  the  difference  on  removing  the  finger. 
Why  would  the  water  not  run  in  at  first  ?   What 
do  you  learn  from  this  experiment  about  water 
and  air? 

As  large  corks  are  usually  very  open,  they 
should  first  be  boiled  in  paraffine.  In  fitting 
corks,  a  flat  wood- file  and  a  small  round  file 
will  be  indispensable. 

38.  Exercise.  —  Make  a  wooden  rectangu- 
lar prism  5  cm.  by  2  cm.  by  20  cm.  In  a  cylin- 
drical jar,  put  100  ccm.  of  water.  Graduate 
the  longest  edge  of  the  prism  to  centimetres. 
Insert  the  bar  vertically  into  the  water.  Mark  on  the  side 
of  the  jar  the  change  of  level  of  the  water ;  then  remove  the 
bar,  and  ascertain  what  volume  of  water  will  produce  the  same 
change  of  level.  How  does  this  volume  compare  with  that 
of  the  part  of  the  bar  submerged?  Repeat  the  experiment 
two  or  three  times,  varying  the  amount  of  the  bar  submerged. 
What  property  does  this  experiment  show  that  matter  pos- 
sesses ? 


FIG.  22. 


39.  Exercise.  —  Adjust  a  U-shaped  delivery  tube  to  a 
bottle  containing  a  known  quantity  of  water,  the  inner  end  of 
the  tube  opening  beneath  the  water,  and  the  outer  end  opening 
within  a  common  tumbler  (Fig.  23).  Pass  through  the  same 
cork  a  funnel-tube  with  a  stop-cock.  All  these  fittings  must  be 
made  air-tight.  For  this  reason,  a  rubber  stopper  is  to  be  pre- 
ferred. Now  shut  off  the  stop-cock,  and  pour  into  the  funnel 
a  measured  quantity  of  water.  Then  turn  the  stop-cock,  and 
let  the  water  pass  into  the  bottle.  Measure  the  water  in  the 


THE  PROPERTIES   OF  MATTER. 


35 


Fw.  23. 


tumbler,  and  compare  the  amount  with  that  poured  into  the 

bottle.      Pour   in    another   known 

quantity,    and    then   ascertain   the 

amount  in  the  tumbler.     Continue 

in  this  way  till  at  least  five  separate 

amounts  of  water  have  been  added 

to  the  bottle.     Find  the  average  of 

the  five  amounts  of   water  poured 

into  the  bottle,  and  also  of  the  five 

amounts  collected  in  the  tumbler. 

Measure  the  amount  of  water  left 

in   the   bottle,    and    correct    these 

averages  by  the  difference  between 

this   amount   and    the    amount   in 

the  bottle  at  the  beginning.     What 

inference  can  you  make  from  comparing  these  averages? 

40.   Exercise.  —  Fit  a  delivery- tube,  and  also  a  funnel- tube 

provided  with  a  stop-cock, 
to  a  well-corked  bottle 
(Fig.  24).  Let  the  deliv- 
ery-tube open  beneath  an 
inverted  cylindrical  grad- 
uate filled  with  water  over 
a  small  pneumatic  trough. 
Pour  a  known  quantity 
of  water  into  the  funnel- 
tube,  opening  the  stop- 
cock as  soon  as  the  air 
has  escaped  from  the 
- 24-  throat  of  the  funnel. 

Measure  the  air  now  found  in  the  graduate.     Repeat  the  opera- 


36  PRACTICAL    PHYSICS. 

tion  several  times,  and  measure  the  air  in  the  graduate  after  each 
pouring.  Each  of  these  results  should  be  corrected  by  subtract- 
ing from  it  the  capacity  of  the  tube  below  the  stop-cock.  Why  ? 
This  capacity  can  be  easily  determined  by  closing  the  end  with 
the  finger,  and  finding  the  amount  of  water  required  to  fill  the 
tube.  Compare  the  amounts  of  water  and  air.  Inference. 

The  funnel-tube  may  be  replaced  by  a  common  funnel  joined 
to  a  glass  tube  by  a  rubber  connector.  A  pinch-cock  (Fig. 
269)  on  the  rubber  will  serve  for  a  stop-cock. 

41.  Exercise.  —  Float  a  cork  on   the   surface   of   water. 
Cover  it  with  a  wide-mouthed  bottle,  and  push  the  glass  vessel, 
mouth  downward,  into  the  water.     What  phenomenon  do  you 
observe?     Insert  one  arm  of  a  U-tube  made  of  glass  tubing 
under  the  edge  of  the  bottle,  and  again  push  it  down  into  the 
water.     Does  the  same  phenomenon  occur  as  before?     What 
do  you  learn  by  holding  a  burning  match  over  the  outer  end  of 
the  U-tube  as  the  vessel  is  pushed  into  the  water?    What  is  the 
lesson  from  this  experiment? 

42.  Exercise.  —  Fill  a  tumbler  level  full  of  water.     Now 
drop  in  carefully,  and  one  at  a  time,  a  number  of  small  nails. 
In  the  fact  that  the  water  does  not  flow  over  the  side  of  the 
vessel,   have  you   an   exception  to  the  principle  that  matter 
is  impenetrable  ?     State  the  evidence  on  which  your  answer  is 
based. 


IV.    DIVISIBILITY. 

43.    Apparatus.  —  The    appliances   needed    are    Balance, 
Weights,  and  Micrometer  Caliper- 


THE  PROPERTIES   OF  MATTER.  37 

44.  Exercise.  —  Put  two  or  three  drops  of  nitric  acid  on  a 
piece  of  copper  ;    let  it  stand  till  the  boiling  action  ceases,  and 
then  wash  it  off  in  a  half -litre  of  clear  water.     To  this  add  a 
few  cubic  centimetres  of  ammonia  water.     The  blue  discolora- 
tion denotes  the  presence  of  copper.     Have  you  any  evidence 
that  copper  is  present  in   every  drop  of  the  liquid?     What 
physical  property  do  you  find  belongs  to  copper?     Determine 
the  amount  of   copper  in  each  cubic  millimetre  of   the  blue 
solution    by  weighing  the  copper  before   applying   the   nitric 
acid,  and  after  washing  it  in  the  water,  and  by  measuring  the 
solution. 

45.  Exercise.  —  Dissolve  .01  gramme  of  an  aniline  dye  in 
one  litre  of  water.     By  dropping  water 

from  a  bottle  or  a  dropper  into  a  gradu- 
ated measure,  ascertain,  by  averaging  five 
trials,  the  number  of  drops  in  a  cubic 
centimetre  of  the  solution.  Now  compute 
how  much  aniline  there  is  in  each  drop  of 
the  colored  solution.  What  property  does 
aniline  possess  to  a  very  marked  extent? 

46.  Exercise.  —  Weigh    accurately   a    clean    silver   coin. 
Place  on  it  two  or  three  drops  of  nitric  acid,  letting  it  remain 
till  the  action  of  the  acid  on  the  silver  ceases.     Then  wash  it 
in  a  tumbler  of  pure  water.     Stir  the  water  thoroughly,  and 
divide  it  into  two  parts.      To  the  one  add  a  few  drops  of  a 
strong  solution  of  common  salt,  and  to  the  other  add  a  few 
centimetres  of  ammonia-water.      Remembering  that  common 
salt  turns  a  solution  of  silver  milky,  and  ammonia-water  turns 
a  solution  of  copper  blue,  what  inference  can  you  draw  from 
the  experiment?     Now  weigh  the  coin,  and  compute  how  much 


38  PRACTICAL   PHYSICS. 

silver  and  how  much  copper  there  is  in  each  cubic  centimetre 
of  the  solution. 

NOTE.  —  American  silver  coin  is  10  per  cent  copper. 

47.  Exercise.  —  Measure  with  a  micrometer  caliper  the  thick- 
ness of  a  piece  of  mica.  Measure  the  thickness  of  the  thinnest 
piece  you  can  split  from  the  original  one.  Is  it  due  to  the  lack 
of  skill,  or  to  some  property  inherent  in  the  mica,  that  you  are 
unable  to  obtain  a  piece  still  thinner? 


V.    POROSITY. 

48.  Apparatus. — For  the  study  of  porosity,  procure  a  Gas- 
Bottle,  a  Three-Necked  Bottle,  some  Glass  Tubing,  a  Common 
Tumbler,  a  Cylindrical  Graduate,  and  a  Florence  Flask. 

49.  Exercise.  —  Determine  whether  rubber  is  porous  or  not. 

Fit  a  deli  very- tube  to  a*gas- 
bottle  (Fig.  26) ,  and  let  it  open 
into  a  three-necked  bottle  in 
which  is  some  water.  Through 
the  middle  neck,  pass  a  long 
glass  tube  reaching  to  the  bot- 
tom of  the  bottle.  Close  the 
third  neck  with  a  perforated 
cork,  through  which  passes  a 
short  piece  of  glass  tubing. 
Now  put  some  zinc  clippings 
in  the  gas-bottle,  and  cover 
PIG.  26.  them  with  dilute  sulphuric  acid, 

one  part  acid  to  three  of  water.     Hydrogen  gas  will  be  given 


THE  PROPERTIES   OF  MATTER.  39 

off,  which  will  pass  over  into  the  second  bottle.  If  you  press 
your  finger  firmly  over  the  end  of  the  tube  in  the  third  neck, 
you  will  notice  that  the  water  will  rise  higher  and  higher  in 
the  second  one  till  it  flows  out  of  the  top  (why?).  Remove 
the  finger,  and  tie  a  small  rubber  balloon  over  the  end  of  the 
tube.  The  water  in  the  second  tube  soon  begins  to  rise,  but 
does  not  get  beyond  a  certain  point,  notwithstanding  that  the 
evolution  of  gas  still  continues  in  the  gas-bottle.  What  be- 
comes of  this  gas?  What  must  be  the  physical  structure  of 
the  rubber? 

All  the  corks  must  be  firmly  tied  down  with  stout  cord  to 
prevent  them  from  being  driven  out  by  the  pressure  of  the 
gas. 

50.  Exercise.  —  Test   a   piece   of    chamois   for   porosity. 
Tie  it  over  the  end  of  a  stout  glass  tube  about 

two- thirds  of  a  metre  long,  and  15  mm.  in  diameter. 
Hold  the  tube  over  a  large  glass  vessel,  and 
with  a  test-glass  (Fig.  27),  or  some  vessel  with 
a  lip,  pour  mercury  into  the  tube,  filling  it  nearly 
full.  What  does  this  experiment  teach  about  the 
structure  of  chamois?  Would  very  fine  shot  sub- 
stituted for  the  mercury  act  in  the  jsame  way  ? 
Why  ?  What  property  of  mercury  is  also  revealed 
in  this  experiment? 

51.  Exercise.  —  Test  thin  sheets  of  several  substances  for 
evidences  of  porosity. 

Select  two  plain  tumblers  of  thin  glass  and  of  the  same  size. 
After  thoroughly  warming  one  of  them,  fill  it  about  half  full  of 
boiling  water.  Now  cover  the  glass  with  a  piece  of  cardboard, 


40 


PRACTICAL   PHYSICS. 


and  invert  the  other  glass  upon  it  (Fig.  28).    After  the  lapse 
of  one  or  two  minutes,  ascertain  if  there  is  any  change  in  the 

condition  of  the  interior  of  the 
upper  tumbler.  What  does 
the  experiment  teach  regarding 
the  structure  of  cardboard? 

Now   re-heat   the   water,  and 
test  in  a  similar  manner  pieces 
of  felt,  chamois,  and  wood.     In 
the  case  of  wood,   ascertain  in 
FlG- 28-  what  manner   a   change   in   the 

thickness  of  the  strip  affects  the  phenomenon. 

52.  Exercise.  —  Fit  to  a  Florence  flask  a  delivery-tube 
leading  to  an  inverted  bottle  standing  over  the  pneumatic 
trough  (Fig.  29).  Fill  the  flask,  tube,  and  inverted  bottle  with 


FIG.  29. 


water,  and  apply  heat  to  the  flask.  After  the  boiling  of  the 
water  has  continued  for  some  time,  remove  the  lamp,  and 
examine  closely  the  collection-bottle.  Whence  the  gas  found 
in  it?  Repeat  the  experiment,  filling  the  apparatus  this  time 


THE  PROPERTIES   OF  MATTER.  41 

with  water  that  has  been  boiled  for  some  time  in  an  open 
vessel.  What  property  does  this  experiment  show  that  water 
possesses  ? 

53.  Exercise.  —  Put  75  ccm.  of  water  in  a  cylin- 
drical graduate.     To  this  add  2  ccm.  of  finely  pow- 
dered sugar.     After  the  sugar  has  dissolved,  observe 
the  volume  of  the  solution.     Account  for  the  shrink- 
age. 

54.  Exercise.  —  In  a   glass   tube   graduated   to 
tenths    of   cubic    centimetres   (Fig.  30),  put  30  ccm. 
of  water.      Then  pour   in  very  gently,   tipping   the 
tube  so  that  it  will  flow  down  the  wall  of  the  tube, 
20  ccm.  of  strong  alcohol.      Hold   the  finger  firmly 
over  the  mouth  of   the  tube,  and  shake  vigorous!}'. 
Observe  the  volume  of   the  mixture.      What  is  the 
percentage  of  shrinkage?     What  has  been  previously 
proved  of  water  that  will  assist  in  explaining  this  phenomenon  ? 


VI.    INDESTRUCTIBILITY. 

55.   Apparatus.  —  The  appliances  needed  are  Test-Tubes, 
Beakers,  Flasks,  and  a  Balance. 


56.  Exercise.  —  Prepare  a  saturated  solution  of 
calcium  chloride  by  adding  the  salt  to  20  ccm.  of  water 
until  it  refuses  to  dissolve  any  more.  Pour  enough  of 
the  solution  into  a  test-tube  (Fig.  31)  to  fill  it  a  little 
less  than  half  full.  In  a  similar  manner,  prepare  an  FIG.  31. 
equal  quantity  of  a  saturated  solution  of  sodium  sulphate  in  a 


42 


PRACTICAL  PHYSICS. 


second  test-tube.  Place  the  test-tubes  in  some  suitable  vessel 
to  prevent  them  from  overturning,  and  determine  their  united 
weight.  Now  pour  one  solution  into  the  other,  and  shake 
quickly.  Observe  the  change  that  takes  place.  Ascertain  if 
the  weight  has  changed. 

Bottles  may  take  the  place  of  the  test-tubes. 

57.  Exercise.  —  Support  a  piece  of  phosphorus  of  the  size 
of  a  small  pea  on  the  end  of  a  wire  of  the  form  shown  in 

Fig.  32.  Put  about  400  ccm. 
of  water  colored  with  blue 
litmus  into  a  thin  beaker  of 
about  one  litre  capacity.  In 
this  place  the  wire  stand  sup- 
porting the  phosphorus,  and 
invert  over  it  a  Florence 
flask,  resting  its  neck  on  the 
edge  of  the  beaker  closing  its 
top,  the  mouth  of  the  flask 
reaching  nearly  to  the  bottom 
of  the  colored  water.  After 

thoroughly  drying  the  outside  of  the  apparatus,  place  it  on 
one  of  the  pans  of  a  balance,  and  exactly  counterpoise  it. 
Let  it  remain  undisturbed  for  twenty-four  hours,  and  then 
examine  the  flask  carefully  to  ascertain  what  changes  have 
taken  place  within  it. 

Would  the  same  weight  be  required  to  counterpoise  the 
apparatus  if  no  phosphorus  had  been  placed  on  the  wire 
support?  Has  the  weight  of  the  beaker  and  its  contents  been 
diminished  by  the  disappearance  of  the  phosphorus?  Have 
the  phosphorus  and  some  of  the  air  in  the  flask  been  de- 
stroyed ? 


FIG.  32. 


THE  PROPERTIES   OF  MATTER.  43 

To  prevent  the  evaporation  of  water  from  the  beaker,  the 
edge  should  be  coated  with  paraffine. 

58.  Exercise.  —  Fill  a  test-tube,  say  2.5  cm.  diameter  and 
15  cm.  long,  with  water  ;  cover  the  mouth  with  the  thumb,  and 
invert    the   tube   in    a   small    beaker 

partly  filled  with  water  (Fig.  33). 
The  tube  should  be  full  of  water,  no 
air  having  been  admitted  in  inverting 
it.  Slip  over  the  tube  a  short  piece 
of  large  glass  tubing,  as  a  piece  of 
lamp-chimney,  to  support  the  test- 
tube  in  a  vertical  position.  Place  a 
small  piece  of  zinc,  say  .05  gramme, 
beneath  the  mouth  of  the  tube.  Pour 
into  a  small  beaker  a  few  centimetres 
of  strong  sulphuric  acid.  Place  the 
vessel  supporting  the  tube,  and  also 

the  beaker  of  acid,  on  the  pan  of  a  fairly  good  balance,  and 
counterpoise  them.  Pour  the  acid  into  the  vessel  supporting 
the  tube,  replacing  the  beaker  in  the  scale-pan.  The  acid  will 
act  on  the  zinc,  and  hydrogen  gas  will  be  seen  to  collect  in 
the  top  of  the  tube.  From  time  to  time,  as  these  changes 
proceed,  set  the  balance  in  action  to  ascertain  if  there  is  any 
gain  or  loss  of  matter.  Inference. 

Caution.  —  If  too  much  zinc  is  used,  the  tube  will  not  hold  all  the 
gas  evolved. 

59.  Exercise.  —  Select  two  thin  glass  beakers,  each  having 
a  capacity  of  about  100  ccm.      Into  one  put  50  ccm.  of  a 
solution  of  lead  nitrate,  and  into  the  other  put  25  ccm.  of 


44  PRACTICAL   PHYSICS. 

a  solution  of  potassium  chromate.  Place  the  two  beakers  on 
the  pan  of  a  balance,  and  counterpoise  them.  Now  pour  the 
contents  of  one  beaker  into  the  other,  restoring  the  beaker  to 
its  place  on  the  scale-pan.  Observe  the  changes  which  occur, 
and  determine  if  they  are  attended  with  any  gain  or  loss  of 
matter. 


VII.    COHESION. 

60.  Apparatus.  —  Bar   of  Lead,  Balance,  Disks   of  differ- 
ent substances,  Funnel  with  Stop-Cock,  Glass   Bulb,  Spring- 
Balance,  Crucible,  Evaporating  Dish,  etc. 

61.  Exercise.  —  Bore  a  hole,  about  2.5  cm.  in  diameter,  in 
a  block  of  wood,  and,  using  it  as  a  mould,  cast  two  disks  of 
lead  2.5  cm.  thick.     Dress  one  surface  of  each  disk  to  a  plane. 
Now  press  the  two  disks  firmly  together,  giving  one  of  them  a 
slight  twisting  motion.     In  this  way,  one  piece  can  be  made  to 
hold  up  the  other.     What  force  is  brought  into  action  ?     What 
do  the  facts  that  pressure,  as  well  as  a  very  smooth  surface, 
is  necessary  to  the  success  of  this  experiment,  teach  regarding 
this  force? 

62.  Exercise.  —  Measure     the     cohesion     of     paper     or 
wire. 

Cut  a  rectangular  piece  of  the  paper  to  be  tested  25  cm.  long 
and  10  cm.  wide.  Fold  over  each  end,  fastening  it  with  glue, 
forming  a  loop  or  hem.  In  these  insert  stout  wooden  rods 
somewhat  longer  than  the  width  of  the  paper.  Connect  the 
ends  of  one  of  these  rods  to  the  hook  of  a  spring-balance  by 
means  of  a  wire  or  cord  bail.  Fasten  the  other  rod  to  some 


THE   PROPERTIES   OF  MATTER.  45 

suitable  support.  Now  pull  steadily  on  the  ring  of  the  balance, 
recording  the  reading  observed  at  the  moment  the  paper  is 
parted. 

Wire  can  be  tested  in  a  similar  manner  by  fastening  one  end 
to  some  firm  object,  and  the  other  end  to  the  hook  of  the 
balance.  Compare  strength  with  the  cross-section.  Ascertain 
if  length  affects  the  strength. 

63.  Exercise.  —  Compare  the  cohesion  of  water,  alcohol, 
glycerine,  etc.,  by  ascertaining  the  degree  to  which  such 
cohesion  affects  the  size  of  falling  drops  of  the  liquid. 

Support  by  a  clamp  a  funnel  provided  with  a  stop-cock  so 
that  its  stem  is  about  1  cm.  above  the  surface  of  a  glass  sphere. 
A  small  Florence  flask  with  a  round  bottom,  or  the  bulb  of  a 
common  air  thermometer,  may  be  used  for  the  sphere.  Pour 
some  of  the  liquid  to  be  tested  in  the  funnel,  and  open  the 
stop-cock  so  that  the  liquid  will  flow  at  such  a  rate  upon 
the  sphere  as  to  drop  from  the  under  surface  at  the  rate  of  two 
drops  per  second.  Now  catch  one  hundred  of  these  drops  in 
a  beaker,  and  determine  their  weight.  Make  at  least  three 
determinations  for  each  liquid. 

Repeat  the  experiment,  changing  the  drop-rate  to  one  in  two 
seconds.  How  is  the  size  of  the  drop  affected? 

Ascertain  the  effect  on  the  drop-size  of  employing  a  smaller 
glass  sphere. 

Record  the  results  as  follows  :  — 

COHESION. 

Problem.  —  Measurements  of  drop-size  of  several  liquids.    Sept.  17, 

1888. 

Method.  —  Weighing  one  hundred  drops  of  liquid. 


46  PRACTICAL   PHYSICS. 

Results.  — 

DROP-RATE, DROP-RATE, 

Water.     Alcohol.  Glycerine.       Water.  Alcohol.  Glycerine. 

First  trial     ....  

Second  "      ....  

Third    " 


Mean 

Weight  of  drop  . 


64.  Exercise.  —  Measure  the  force  necessary  to  pull  a  disk 
away  from  a  liquid. 

Remove  one  of  the  scale-pans  from  a  balance,  —  the  jew- 
eller's form  answers  the  purpose  nicely,  —  and  suspend  in  its 
place  a  glass  disk,  about  5  cm.  diam- 
eter, by  means  of  three  threads  at- 
tached at  points  120  degrees  apart 
(Fig.  34).  After  accurately  counter- 
poising the  disk,  place  a  vessel  of 
water  below  it,  raising  it  till  the  sur- 
face of  the  water  touches  the  under 
surface  of  the  disk,  being  careful  to 
keep  the  beam  horizontal.  Now  add 
weights  to  the  scale-pan  till  the  disk 

is  pulled  away  from  the  water.  These  weights  must  not  be 
dropped  into  the  pan,  as  the  sudden  jar  would  tend  to  separate 
the  disk  from  the  water.  Ascertain  whether  you  have  pulled  a 
column  of  water  apart,  or  pulled  the  plate  away  from  the  water. 
Measure  the  disk,  and  then  compute  the  force  per  square 
centimetre  required  to  effect  the  separation. 

The  disk  must  be  perfectly  clean,  and  in  bringing  it  in 
contact  with  the  liquid,  first  touch  one  edge,  and  then  gradually 
shut  down  the  disk  upon  the  liquid,  thus  excluding  all  air 


THE  PROPERTIES   OF  MATTER.  47 

bubbles,  and  insuring  good  contact.  The  threads  can  be 
attached  to  the  disk  by  means  of  tough  sealing-wax.  See 
Art.  607. 

Try  other  liquids,  as  mercury,  alcohol,  glycerine,  etc. 

Try  successively  disks  made  of  brass,  tin,  zinc,  etc. 

Amalgamate  these  disks  with  mercury  before  measuring  the 
force  required  to  separate  them  from  mercury. 

Measure  the  force  required  to  separate  from  water  a  glass 
disk  coated  with  a  film  of  sweet  oil. 

Construct  a  comparative  table  of  all  the  results. 

65.  Exercise.  —  Select  a  soft  glass  tube  about  25  cm.  long 
and  2  cm.  in  diameter.      Close  one  end   in   the   flame   of  a 
blow-pipe,   and   then   bend   the   tube   to   a  V  shape   with   its 
branches   widely   diverging,    and    the   closed   arm   3   cm.  the 
longer.     Nearly  fill  the  tube  with  water,  and  boil  it  uniformly 
till  nearly  a  quarter  has  boiled  away.     Remove  the  flame,  and 
close  the  open  end  air-tight  with  a  rubber  stopper.   When  cold, 
hold  the  hand  against  the  end  of  the  long  arm  ;  let  the  water 
in  the  tube  fall  against  it.     The  water  will  be  found  to  remain 
suspended  in  that  arm  on  holding  it  in  a  vertical  position, 
instead  of  falling  back  to  the  level  of  the  water  in  the  other 
arm,  requiring  quite  a  jar  to  break  it  away  from  the  end  of  the 
tube.     Explain. 

66.  Exercise.  —  Dissolve  100  grammes  of  powdered  alum 
in  half   a  litre  of   hot  water.      Hang  in  the  solution  strings, 
twigs  of  plants,  or  wire  forms,  and  set  aside  for  twelve  hours. 
Make  a  careful  study  of   the   alum  crystal.      Diagram  one. 
Copper  sulphate  may  be  substituted  for  the  alum.     Make  a 
mixture  of  the  two  solutions  in  an  evaporating  dish  or  saucer, 
and  set  aside  till  crystallization  occurs. 


48  PRACTICAL   PHYSICS. 

67.  Exercise.  —  Wet  the  surface  of  a  strip  of  glass  with  a 
solution  of  ammonium  chloride.     As  it  begins  to  dry,  examine 
it  carefully  under  a  microscope.     A  good  botanizing-glass  will 
answer  the  purpose. 

68.  Exercise.  —  Melt  a  quantity  of  sulphur  in  a  Hessian 
crucible  or  common  tea-cup.     The  vessel  should  be  at  least 
two-thirds  full.     As  soon  as  the  sulphur  is  melted,  set  it  aside 
to  cool,  leaving  it  till  a  thin  crust  forms  over  the  top.     Now 
break   through   the   crust,   and   pour  out  the   liquid   interior. 
Examine  with  a  common  magnifier  the  interior  of  the  cavity, 
determining  the  form  of  the  crystals. 

69.  Exercise.  —  Prepare  a  saturated  solution  of  common 
salt.     Pour  the  solution  into  a  common  saucer  or  an  evaporat- 
ing dish,  and  set  it  aside  protected  from  dust.     In  a  few  days, 
the  bottom  of  the  dish  will  be  covered  with  crystals  curiously 
grouped.     Make  a  close  study  of  the  shape  of  the  crystals,  and 
the  manner  of  grouping. 

By  observing  the  following  directions,  quite  large  salt  crystals 
can  be  obtained  :  — 

"  The  salt  to  be  crystallized  is  to  be  dissolved  in  water,  and 
evaporated  to  such  a  consistency  that  it  shall  crystallize  on 
cooling.  Set  it  by,  and  when  quite  cold,  pour  the  liquid  part 
from  the  mass  of  crystals  at  the  bottom  into  a  flat-bottomed 
vessel.  Solitary  crystals  will  form  at  some  distance  from  each 
other,  and  gradually  increase  in  size.  Pick  out  the  most 
regular,  put  them  into  another  flat-bottomed  vessel  a  little 
apart  from  each  other,  and  pour  over  them  a  quantity  of  fresh 
solution  of  the  salt  evaporated  till  it  crystallizes  on  cooling. 
Alter  the  position  of  every  crystal  once  at  least  every  day  with 
a  glass  rod,  that  all  the  faces  may  be  alternately  exposed  to 


THE  PROPERTIES   OF  MATTER.  49 

the  action  of  the  liquid,  for  the  face  on  which  the  crystal  rests 
never  receives  any  increase.  By  this  process,  the  crystals  will 
gradually  augment  in  size.  When  they  have  acquired  such  a 
magnitude  that  their  forms  can  easily  be  distinguished,  the 
most  regular  are  to  be  chosen,  or  those  which  have  the  exact 
shape  which  you  wish  to  obtain.  Each  of  them  should  be  put 
separately  into  a  vessel  filled  with  a  portion  of  the  same  liquid, 
and  turned  by  the  glass  rod  several  times  a  day.  Whenever  it 
is  observed  that  the  angles  and  edges  of  the  crystals  become 
blunted,  the  liquid  must  immediately  be  poured  off,  and  fresh 
liquid  put  in  its  place ;  otherwise  the  crystals  will  be  infallibly 
destroyed." 

70.  Exercise.  —  Procure  pieces  of  mica,  Iceland  spar,  roll 
sulphur,  common  white  chalk,  alum,  coal,  feldspar,  blue  vitriol, 
sal  ammoniac,  galena,  pyrites,  etc.     With  a  knife,  try  to  split 
these  substances  in  different  directions.    What  do  you  discover 
with  respect  to  the  relative  ease  of  breaking  or  splitting  each 
of  these  substances  in  different  directions  ?     Study  closely  the 
surfaces  exposed  at  each  separation,   and  see  if  it  indicates 
the  breaking-up  of  a  structure,  or  the  splitting-apart  of  two  or 
more  complete  structures.     Examine  the  corners;  in  short,  note 
every  thing  having  any  bearing  on  the  molecular  structure  of 
the  substance. 

71.  Exercise.  —  Classify   a   number   of    substances    with 
reference  to  their  hardness  on  Mohr's  scale. 

Mohr's  scale  is  the  hardness  of  the  following  ten  substances, 
which  are  ranked  as  shown  by  the  attached  numbers  :  1 ,  talc  ; 
2,  gypsum;  2.5,  mica;  3,  calcite ;  4,  fluor-spar  ;  5,  apatite  ; 
5.5,  scapolite  ;  6,  feldspar  ;  7,  quartz  ;  8,  topaz  ;  9,  sapphire  ; 
10,  diamond. 


50  PRACTICAL  PHYSICS. 

To  determine  the  hardness  of  any  substance,  draw  a  file  over 
it  with  considerable  pressure,  and  observe  whether  the  depth  of 
the  cut  made  in  the  specimen  is  greater,  less,  or  equal  to,  that 
made  in  some  one  of  the  minerals  of  the  scale.  If,  for 
instance,  the  cut  made  in  the  substance  is  less  than  that  made 
in  6,  and  deeper  than  that  made  by  the  same  pressure  of  the 
file  in  7,  it  ranks  in  hardness  between  6  and  7. 

Glass,  slate,  marble,  gypsum,  galena,  hematite,  magnetite, 
fluor-spar,  copper,  silver,  steel,  etc.,  are  some  of  the  substances 
easily  obtained  for  the  purposes  of  this  experiment. 

VIII.    ELASTICITY. 

72.  Apparatus.  —  The  appliances  required   for  studying 
elasticit}^  are  such  as  any  one  accustomed  to  the  use  of  tools 
can  readily  make  by  following  the  directions  given.     A  stock 
of  wires,  wooden  bars,  and  metal  and  wooden  rods  of  various 
sizes  and  numbers,  will  be  needed  for  testing. 

73.  Exercise.  —  Study  the  elasticity  of  solids  when  mani- 
fested by  pressure. 

Procure  several  balls,  one  each,  of  wood,  glass,  ivory,  etc., 
each  having  a  diameter  of  about  2  cm.  Drop  them  from  the 
same  height  on  a  marble  slab,  and  compare  the  heights  to 
which  they  rebound.  Double  the  height,  and  repeat  the  com- 
parison. Triple  the  height,  and  compare.  Now  repeat  the 
experiment,  having  coated  the  slab  with  a  thin  film  of  paste 
made  of  olive-oil  and  common  whiting  thoroughly  mixed 
together.  Compare  the  marks  made  in  the  film  by  the  balls 
when  merely  laid  on  the  marble,  with  those  made  when  the 
balls  fall  from  a  height.  What  inference  follows  respecting 
the  various  substances  of  which  the  balls  are  made  ? 


THE   PROPERTIES   OF  MATTES. 


51 


74.  Exercise.  —  Show  that  the  amount  of  extension  of  a 
wire  is  proportional  to  its  length,  and  to  the  weight  which 
produces  the  extension,  within  certain  limits,  and  is  inversely 
as  the  cross-section. 


FIG.  35. 

Construct  a  stout  wooden  frame  of  the  form  shown  in 
Fig.  35,  having  the  upright  at  least  one  metre  high.  Attach 
to  it  a  millimetre  scale.  Suspend  in  succession  straight  pieces 
of  iron,  steel,  copper,  brass,  etc.  wires  of  the  same  size,  from 
a  hook  on  the  under  side  of  the  arm  at  the  top  of  the  vertical 
support,  fastening  to  the  lower  end  a  scale-pan  made  of  tin  or 
brass.  Fasten  to  the  wire  two  pointers,  A  and  B,  and  record 
the  difference  in  the  readings  for  the  length  AB.  Now  put 
some  known  weights  in  the  pan,  and  again  determine  AB.  Add 
more  weights,  and  again  read  the  distance  AB.  Continue 


52  PRACTICAL   PHYSICS. 

doing  this,  if  possible,  till  the  wire  breaks.  After  each  reading 
is  taken,  remove  all  the  weights,  and  record  the  length  of  the 
wire.  Tabulate  the  results.  Compare  the  increase  in  length 
each  time  with  the  total  weight  in  the  pan,  and  you  should  find 
that  the  wire  has  increased  in  length  proportionally  to  its  length, 
and  to  the  load  in  the  pan,  up  to  a  certain  point ;  also,  that  the 
wire  has  returned  each  time  to  its  original  length  up  to  the  same 
point,  and  that  beyond  that  point,  known  as  the  limit  of 
elasticity,  the  elongation  is  not  uniform. 

Repeat  the  experiments,  employing  a  wire  of  somewhat 
larger  cross-section,  and  make  the  same  changes  in  the  weights. 
Compare  the  effects  on  length  with  those  previously  determined. 
Inference. 

Construct  a  curve  from  the  data  obtained,  and  point  out 
how  it  proves  the  law.  For  method  of  constructing  curve,  see 
Art.  598. 

75.  Exercise.  —  Determine  the  laws  governing  the  deflec- 
tion of  beams. 

Construct  of  wood  an  apparatus  such  as  shown  in  Fig.  36. 
A  and  B  are  pyramidal  pieces  of  hard  wood  20  cm.  high,  stand- 
ing on  the  base  N,  the  distance  between  their  upper  edges  being 
determined  by  means  of  the  linear  scale  S.  M  is  a  bar,  wood 
or  metal,  1  metre  long,  2.5  cm.  wide,  and  5  cm.  thick,  whose 
deflection  is  to  be  measured.  C  is  a  small  clevis  made  of  sheet 
brass,  placed  exactly  over  the  centre  of  the  bar,  supporting  the 
scale-pan  F.  RLE  is  a  bent  lever  made  of  wire,  the  weight  of 
which  is  sufficient  to  keep  its  foot  in  close  contact  with  C  as  the 
bar  M  deflects.  Narrow  grooves  filed  in  the  wire  on  top  of 
the  post  H  will  make  it  easy  to  secure  it  in  place  by  means 
of  wire  staples.  Freedom  of  motion  must  be  secured  with  as 
little  play  as  possible.  K  is  a  scale  of  equal  parts. 


THE  PROPERTIES   OF  MATTER. 


53 


Record  the  reading  of  the  pointer,  then  keep  adding  weights 
and  recording  the  reading  till  a  sufficient  number  have  been 
made  for  comparison.  Compare  the  amount  of  deflection  with 
the  weights  applied. 

Try  a  bar  of  the  same  material,  having  double  the  breadth, 
and  the  same  thickness  as  the  first.  Inference.  Try  one 


FIG.  36. 


having  double  the  depth,  and   the  same  width  as  the  first. 
Inference.      Try  one  having  double  the  length,  but  the  same 
width  and  thickness  as  the  first.     Inference. 
Construct  a  curve  from  the  data. 


76.   Exercise.  —  Determine  the  laws  of  elasticity  by  torsion. 

Construct  of  wood  an  apparatus  such  as  is  shown  in  Fig.  37, 
making  L  90  cm.  long.  W  is  the  wire  to  be  experimented  on, 
the  upper  end  being  squared,  and  fitted  snugly  into  a  metal 
plate  A  to  keep  it  from  turning,  the  lower  end  passing  through 


54 


PRACTICAL  PHYSICS, 


the  pulley  E,  and  entering  a  round  hole  in  the  base  M.  The 
pulley  is  made  with  a  hub,  so  that  a  set  screw  can  be  used  to 
clamp  it  rigidly  to  the  wire.  F  is  a  pointer  moving  over  the 
arc  D.  H  and  K  are  common  iron  pulleys,  over  which  cords 

from  the  pulley  E  draw  so 
that  weights  placed  in  the 
pans  twist  the  wire  or  rod. 
The  shelves  B  and  C  are 
placed  so  that  the  spaces 
AB,  BC,  and  CD  are  each 
equal  to  30  cm.  Observe 
the  reading  of  each  pointer, 
then  place  equal  weights  in 
the  pans,  and  observe  the 
change  in  the  readings. 
Compare  the  change  at  B 
with  that  at  C  and  at  D. 
How  does  length  affect  the 
amount  of  twist?  Increase 
the  weights  in  the  pans,  and 
determine,  from  the  change 
in  the  readings,  how  the 
force  applied  affects  the 
twist.  Substitute  for  W  a 
rod  of  the  same  material  having  a  different  diameter.  Use 
the  same  weights,  and  determine  how  a  change  in  diameter 
affects  the  amount  of  twist. 


Pi«.  37. 


THE  PROPERTIES   OF  MATTER.  55 


IX.     CAPILLARY    ACTION. 

77.  Apparatus.  —  Sewing-Needles,  small  Wooden  Balls, 
Iron  Wire,  Soap  Solution,  Glass  Rod,  Glass  Plates,  Capillary 
Tubes,     Tumbler,     Earthen     Plate,     Balance,     Linear     Scale, 
etc. 

C:> 

78.  Exercise.  —  Place  a  sewing-needle  on  the  surface  of  a 
vessel  of  water.      If  carefully  done,  it  will  float.     A  hairpin 
bent  up  slightly  at  the  points  may  be  used  to  advantage  in 
letting  down  the  needle  so  that  its  two  ends  touch  the  water 
about   simultaneously.      Observe   carefully   the   shape   of   the 
surface  of  the  water  about  the  needle.      Estimate  as  well  as 
you  can  the  area  of  the  cross-section  of  the  depression  as  com- 
pared with  that  of  the  needle.     A  body  floats  on  water  when  it 
displaces  a  volume  whose  weight  equals   that   of   the   body. 
Does  the  needle  do  it? 

Place  two  needles  on  the  water  in  positions  parallel  to  each 
other,  and  separated  by  a  few  millimetres.  Let  a  drop  of 
alcohol  or  ether  fall  on  the  water  between  them,  and  note  the 
effect. 

If  the  surface  of  the  water  is  covered  with  a  powder  called 
lycopodium,  quite  large  wires  can  be  floated. 

79.  Exercise.  —  Float  two  wooden  balls,  of  about  15  mm. 
diameter,  near  each  other  on  water.     Their  surfaces  should  be 
freed  from  all  oily  matter  by  washing  them  with  a  solution  of 
caustic  potash.     Observe  the  shape  of  the  surface  of  the  water, 
and  notice  how  the  balls  act  toward  each  other.     When  quite 
close  together,  let  fall  a  drop  of  alcohol  on  the  water  between 
them. 


56 


PRACTICAL  PHYSICS. 


Coat  one  of  the  balls  with  a  thin  film  of  lard,  and  repeat  the 
experiment.     Study  the  shape  of  the  water  surface. 
Repeat  after  coating  both  balls  with  lard. 

80.  Exercise.  —  Construct  of  No.  24  iron  wire  a  ring 
6  cm.  in  diameter,  a  tetrahedron  4  cm.  on  each  edge,  and  a 
cube  5  cm.  on  each  edge,  each  wire  form  having  a  handle 
attached  (Fig.  38).  In  400  ccm.  of  cold  water  that  has  been 


FIG.  38. 

previously  boiled,  put  10  grammes  of  Castile  soap  cut  up  fine, 
or,  better  still,  sodium  oleate.  Put  this  into  a  bottle,  and 
set  it  in  hot  water  over  a  gas  flame  turned  low  so  as  to  keep 
the  temperature  about  constant.  Let  it  remain  there  an  hour, 
shaking  it  occasionally  till  the  soap  is  dissolved.  Set  aside 
for  several  hours  in  a  place  where  it  will  not  be  disturbed,  and 
then  pour  off  the  clear  liquid,  and  add  to  it  270  ccm.  of  the  best 
glycerine,  shaking  the  whole  thoroughly.  Suspend  in  the  wire 


THE  PROPERTIES   OF  MATTER.  57 

ring  a  small  loop  of  fine  silk  thread,  and  dip  it  into  this  soap 
solution.  Break  the  film  in  the  silk  loop  by  puncturing  it  with 
a  hot  wire,  or  a  piece  of  blotting-paper,  and  account  for  the 
shape  it  takes.  Dip  the  other  wire  forms  in  this  solution, 
and  study  the  film  forms  obtained.  Blow  a  soap-bubble  with  a 
common  clay  pipe,  detach  the  bubble,  and  support  it  on  the 
wire  ring.  Bring  in  contact  with  the  bubble  a  second  ring,  and 
you  will  be  able  to  draw  out  the  bubble  into  a  cylinder. 

81.  Exercise.  —  It  is  required  to  measure  the  tension  of  a 
soap  film. 

Support  horizontally  a  knitting-needle  or  stout  wire,  AB 
(Fig.  39).  Cut  from  a  straight,  slender  straw  a  piece  of 
uniform  size  and  10  cm.  long,  as  CD.  Attach  to  one  side 
and  at  the  ^ 

centre,    a        i  i.mt».»»»u»L» ,...^^ .....................  o 

light  scale-  C • 

pan  made  of 

paper.  Find 

the    weight 

of  the  straw  FIG.  39. 

and  the  attached  pan. 

Hold  the  straw  against  the  under  side  of  the  knitting-neeaie, 
and  with  a  small  brush  introduce  a  layer  of  the  soap  solution 
between  them.  The  tension  of  the  film  will  now  support  the 
straw.  Carefully  sift  fine  sand  on  the  pan  till  the  film  breaks. 
The  weight  of  the  sand,  straw,  and  pan  measures  approximately 
the  tension  of  the  film.  This  divided  by  twice  CD  will  give 
the  superficial  tension  of  either  surface  per  unit  of  length. 

82.  Exercise.  —  Study  the  effect  of  a  solution  of  camphor 
on  surface  tension  by  placing  a  piece  of  camphor  of  the  size 
of  the  head  of  a  pin  on  clean  cold  water,  and  noticing  its 


58  PRACTICAL  PHYSICS. 

peculiar  movements.  Touch  the  water  with  the  finger,  slightly 
oiled  by  rubbing  it  on  the  hair,  and  mark  the  effect.  Using 
clean  water,  study  the  movements  of  a  drop  of  a  solution  of 
camphor  in  sulphuric  acid.  Add  other  drops,  and  observe  their 
behavior  towards  one  another.  Using  clean  water,  study  the 
action  of  a  drop  of  a  solution  of  camphor  in  benzole.  Repeat 
all  of  these  experiments,  using  warm  water  in  place  of  cold. 

The  effect  of  camphor  films  on  the  surface  tension  can  be 
learned  by  covering  the  surface  of  the  water  with  lycopodium 
powder,  then  lowering  a  fragment  of  camphor  into  the  water, 
and  observing  the  effect  that  the  camphor's  touching  the 
water  has  on  the  powder. 

83.  Exercise.  —  Suspend,  by  a  thread,   from  a  suitable 
support,  a  glass  rod,  so  that  the  lower  end  dips  into  a  tumbler 
of  water  colored  with  aniline  dye  or  ink,  the  rod  having  a 
vertical  position.     Study  the  form  of  the  surface  of  the  water 
around  the  rod. 

Repeat  the  experiment,  using  a  glass  rod  thinly  coated  with 
oil. 

Repeat  these  experiments,  substituting  mercury  for  water. 

Thoroughly  clean  a  strip  of  zinc  by  scouring  it  with  a  cloth 
after  it  has  stood  a  few  minutes  in  dilute  sulphuric  acid. 
Suspend  it  vertically  in  a  dish  of  mercury. 

Diagram  the  appearance  of  the  surface  of  the  liquid  about 
the  rod  in  each  of  these  experiments. 

Lift  the  rod  slowly  out  of  the  liquid,  observe  the  liquid  just 
as  the  end  of  the  rod  separates  from  it,  and  then  see  if  you  can 
account  for  the  various  results  obtained  in  these  experiments. 

84.  Exercise.  —  Cut  two  plates   of  glass   about   10  cm. 
square,  and  thoroughly  clean  them,     In  a  large  dinner-plate, 


THE  PROPERTIES   OF  MATTER.  59 

pour  some  water  highly  colored  with  ink  or  aniline  dye. 
Support  one  of  the  plates  in  a  vertical  position  in  the  liquid. 
Examine  the  surface  of  the  liquid  about  the  plate.  Now  place 
in  the  liquid  the  second  plate,  securing  it  in  a  position  parallel 
to  the  first,  and  separated  from  it  by  about  5  mm.  Note 
the  position  of  the  surface  of  the  liquid  between  the  plates. 
Determine  the  effect  of  decreasing  the  distance  between  the 
plates. 

Vary  the  experiment  by  making  the  plates  touch  along  two 
vertical  edges,  the  opposite  ones  being  separated  by  about 
2  mm.  This  is  readily  done  by  fitting  a  piece  of  wood  between 
the  two  edges  to  be  kept  apart,  and  then  slipping  an  elastic 
band  around  the  two  plates. 

85.   Exercise.  —  Determine  the  laws  of  capillary  action. 

Cut  three  capillary  tubes  of  different  diameters,  10  cm.  long. 
Measure  their  diameters  as  in  Art.  34.  Construct  a  paper 
scale  graduated  to  half -millimetres,  cutting  one  end  to  a 
V  shape,  the  zero  of  the  scale  being  the  point  of  the  V.  Coat 
the  scale  with  transparent  varnish,  or  with  a  thin  film  of 
paraffine.  Fasten  a  tube  to  the  scale  by  means  of  rubber 
bands,  and  then  support  the  apparatus  in  a  vertical  position  so 
that  the  tube  dips  into  water,  the  zero  of  the  scale  just  touching 
the  water.  Now  raise  the  vessel  containing  the  liquid  about 
1  cm.,  and  then  lower  it  to  its  original  position  in  order  to 
wet  the  interior  of  the  tube  with  the  liquid.  Using  a 
pocket  lens  to  insure  greater  accuracy,  read  off  the  height 
of  the  liquid  in  the  tube.  This  reading  should  be  taken 
to  the  bottom  of  the  meniscus,  and  increased  by  one-sixth 
of  the  diameter  of  the  tube.  When  the  heights  have  been 
ascertained  for  the  different  tubes,  multiply  each  result  by  the 
diameter  of  the  corresponding  tube.  If  the  measurements 


60 


PRACTICAL   PHYSICS. 


have  all  been  carefully  made,  the  products  will  be  found  to  be 
nearly  equal.  What  law  of  capillarity  is  here  shown? 

Using  one  of  the  tubes,  determine  the  heights  to  which  the 
following  liquids  rise  :  alcohol,  benzine,  turpentine,  etc.  The 
tube  must  be  thoroughly  cleaned  after  each  experiment  (see 
Art.  34) ,  and  the  inner  surface  must  also  be  wet  with  the  liquid 
employed,  as  was  done  in  the  case  of  water. 

A  strip  of  plain  sheet-metal  may  be  used  instead  of  the 
graduated  paper  scale.  The  position  of  the  lowest  point  of 
the  meniscus  might  then  be  carefully  marked  on  it  with  a 
sharp-pointed  instrument,  and  the  distance  afterwards  meas- 
ured with  the  dividers  and  scale. 

Enter  the  results  in  the  note-book  as  follows :  — 


CAPILLARY    MEASUREMENTS. 

Problem.  —  Determination  of  laws  governing  capillary  action.  Sept. 
20,  1888. 

Method.  —  [To  the  pupil.  —  Give  brief  summary  of  the  process 
used.] 

Results.  — 


a 

& 

jj 

— 

>> 

3 

1 

8 

4 
I 

«s 

V 

1 

2 
• 

il 

r 

Weight  of  Vess 

>  3 
U 

11 

bflT3 

|S 

Weight  of  Merc 

Area  of  Cross-S( 

Diameter  of  Tu 

Height  Water  ri 

Height  correctec 
Meniscus. 

Product  of  Dian 
by  Height. 

First  tube     .... 

Second  tube      .    .    . 

Third  tube   .... 

THE  PROPERTIES   OF  MATTER.  61 


X.    SOLUBILITY. 

86.  Apparatus.  —  Small    Flasks,    Test-Tubes,    Thermom- 
eter, and  Balance. 

87.  Exercise.  —  Determine  the  solubilit}^  of  a  substance, 
that  is,   the  number  of  grammes  which  one  gramme  of    the 
solvent  will  dissolve,  the  solution  to  be  saturated. 

Fill  a  small  flask,  or  a  large  test-tube,  half  full  of  the  solvent. 
Add,  in  a  powdered  state,  a  quantity  of  the  substance  to  be 
dissolved,  being  sure  to  add  more  than  will  dissolve.  Now 
raise  the  temperature  somewhat  higher  than  that  at  which  the 
solubility  is  to  be  determined  ;  if  water,  it  may  be  brought 
to  the  boiling-point.  When  the  undissolved  part  no  longer 
diminishes  in  quantity,  remove  from  over  the  source  of  heat, 
and  cool  it  to  the  required  temperature  by  placing  the  vessel  in 
melting  ice.  When  the  required  temperature  is  reached,  drop 
in  the  solution  a  crystal  of  the  substance,  and  there  will  be 
precipitated  all  the  salt  in  solution  over  and  above  that  held  in 
solution  at  the  saturation  point.  Pour  off  into  a  small  Florence 
flask  of  known  weight  some  of  this  solution,  weigh  it  accurately, 
and  then,  by  placing  it  on  a  sand-bath,  over  a  lamp  or  steam- 
coil,  evaporate  all  the  water,  even  that  of  crystallization,  being 
careful  not  to  hasten  too  rapidly  the  evaporation  for  fear  of 
loss  of  material  through  "  spitting."  When  thoroughly  dry, 
weigh  the  residue,  and  obtain  the  weight  of  the  substance 
dissolved.  Divide  the  weight,  in  grammes,  of  the  amount  of 
the  substance  dissolved,  by  the  amount  of  the  solvent 
evaporated  out  of  the  solution,  and  the  solubility  of  the 
substance  is  obtained. 


62  PRACTICAL  PHYSICS. 

88.  Exercise.  —  Find  the  solubility  of   alum  in  water  at 
0°  C.,  20°  C.,  40°  C.,  etc.,  to  100°  C.     Construct  the  curve  of 
solubility.     See  Art.  598. 

89.  Exercise.  —  Find  the  solubility  of  potassium  chloride 
in  water  at  0°  C.,  20°  C.,  40°  C.,  etc.,  to  100°  C.     Construct  the 
curve  of  solubility. 

90.  Exercise.  —  Determine  the  solubility  of  potassium  ni- 
trate in  water  at  0°C.,  20° C.,  40° C.,  etc.,  to  100°C.    Construct 
the  curve  of  solubility. 

91.  Exercise.  —  Determine  the  solubility  of  common  salt 
in  water  at  0°  C.,  20°  C.,  40°  C.,  etc.,  to  100°  C.     Construct  the 
curve  of  solubility. 

92.  Exercise.  —  Determine  the  solubility  of  alum,  potas- 
sium chloride,  potassium  nitrate,  and  common  salt,  in  alcohol 
(95  per  cent),  at  20°  C. 

93.  Exercise.  —  Determine    the    solubility  of    potassium 
sulphate  in  water  at  the  temperature  of  the  room  ;    also  of 
sodium  nitrate.      Finally,  determine  the  solubility  of  sodium 
nitrate  in  the  saturated  solution  of  potassium  sulphate. 


THE  PROPERTIES   OF  MATTER. 


63 


XI.    DIFFUSION. 

94.  Apparatus.  —  Test-Tubes,  Thistle-Tubes,  Battery-Jar, 
Four-Ounce  Bottle,  Parchment  Paper,  Dialyzer,  Porous  Cup, 
Large  Glass  Tube,  Sheet  Rubber,  etc. 


full  of 
in   the 


95.    Exercise.  —  Fill  a  large  test-tube  two-thirds 
water  colored  with  blue  litmus.      Place  a  thistle-tube 
test-tube  (Fig.  40),  having  it  reach  to  the  bot- 
tom, and  pour  into  it  a  few  drops  of  sulphuric 
acid.      A   reddish    color   will    be    seen    at    the 
bottom  of   the  test-tube.      Set  the  test-tube  to 
one  side,   and  record,   from  time  to  time,   the 
position  of  the  upper  surface  of  the  red-colored 
liquid. 

Into  a  common  test-tube,  pour  a  little  blue 
litmus  solution,  and  add  to  it  a  drop  of  sulphuric 
acid  by  stirring,  observing  the  effect  on  the 
color.  Apply  the  truth  taught  by  this  to  the  ex- 
planation of  the  first.  Account  for  the  surface 
which  separates  the  colored  liquids  not  being 
stationary. 


96.   Exercise.  —  Measure  the  Tate  of  diffu- 
sion of  a  substance  in  water. 

Obtain  a  cylindrical  vessel  of   about  2  litres 
capacity,  —  a  common  battery-jar  will  answer;  a 
wide-mouthed  bottle  of  about  4  ounces  capacity,  to  be  known 
as  the  diffusion-bottle  ;  and  a  solution  of  the  salt  under  investi- 
gation of  some  known  strength,  say,  6  parts  by  weight  in  100 
parts  of  water. 


64  PRACTICAL   PHYSICS. 

Fill  the  diffusion-bottle  with  the  solution  to  be  tested  up  to 
the  brim,  and  place  it  on  the  bottom  of  the  large  cylindrical 
jar.  Then  pour  water  into  this  jar  till  it  rises  about  3  mm. 
above  the  top  of  the  diffusion-bottle  (Fig.  41).  Let  the 
apparatus  remain  undisturbed  for  twenty- 
four  hours,  and  at  a  constant  temperature. 
Then,  by  means  of  a  siphon,  run  off  the 
contents  of  the  jar  into  a  basin,  in  which 
wash  off  the  outside  of  the  diffusion-bottle 
by  means  of  a  little  jet  of  pure  water,  first 
taking  the  precaution  to  place  a  small  plate 
of  glass  over  the  mouth  so  as  not  to  spill 
any  of  its  contents  into  the  basin.  Evaporate 
to  dry  ness  the  solution  in  the  basin,  and  determine  the  weight 
of  the  residue.  Comparing  this  with  the  result  obtained  by 
using  a  solution  of  some  other  salt  of  the  same  strength  will 
give  their  relative  diffusion. 

97.  Exercise.  —  Compare  the  rates  of  diffusion  of  potassium 
chloride  and  potassium  sulphate. 

98.  Exercise.  —  Ascertain  if  the  strength  of  the  solution  in 
any  way  affects  the  rate  of  diffusion  by  using  four  solutions  of 
common  salt  made  by  dissolving  1,  2,  3,  and  4  parts  of  salt  in 
100  parts  of  water  by  weight. 

These  four  solutions  may  be  tested  simultaneously  by  select- 
ing jars  and  bottles  of  the  same  size.  The  diffusion-bottles 
especially  must  have  the  same  capacity,  and  the  openings  must 
be  of  the  same  size. 

99.  Exercise.  —  Wet  a  piece  of  parchment  paper,  and  tie 
it  across  the  top  of  a  large  thistle-tube.     Pour  down  the  stem 


THE  PROPERTIES   OF  MATTER. 


65 


of  the  thistle- tube  a  concentrated  solution  of  copper  sulphate, 
spilling  none  on  the  outside  of  it.  Now  support  the  tube  by 
means  of  a  burette-holder  in  a  beaker  of  water,  so  as  to  have 
the  liquids  at  the  same  level  on  both  sides  of  the  tube  to  prevent 
hydrostatic  pressure.  Set  aside  for  a  few  hours,  occasionally 
observing  the  relative  levels  of  the  two  liquids.  Explain. 

100.  Exercise.  —  Set  up  an  apparatus  similar  to  that  of 
the  last  experiment,  and  substitute  a  thin  starch  paste  for  the 
salt  solution.  Ascertain  whether  any  of  the  starch  passes 
through  the  parchment  by  testing  the  water  on  the  outside 
with  iodine  water.  A  blue  color  would  indicate  that  there  was 
starch  present.  Iodine  water  is  made  by  dissolving  iodine  in 
water. 


101.    Exercise.  —  Separate   a  mixed  solution   of   common 
salt  and  starch. 

Make  a  wooden  hoop  about  8  cm. 
in  diameter  and  5  cm.  deep.  Stretch 
across  it  a  piece  of  parchment  paper, 
making  a  shallow  tray.  Such  an  ap- 
paratus is  known  as  a  Dialyzer.  Pour 
the  given  mixture  into  this  tray,  and 
float  it  on  pure  water  in  a  large  battery- 
jar  or  suitable  vessel.  Set  aside  for  a 
few  da}rs,  and  then  test  the  liquid  in 
the  jar  for  starch,  as  in  Art.  100,  and 
also  for  salt,  by  adding  a  little  of  it  to 
a  dilute  solution  of  silver  nitrate.  A  flocculent  white  precipitate, 
changing,  when  exposed  to  light,  to  a  dirty  pink  color,  would 
indicate  the  presence  of  salt.  Pure  distilled  or  rain  water  must 
be  used. 


FIG.  42. 


66 


PRACTICAL   PHYSICS. 


A  good  form  can  be  made  by  cutting  off  a  large  bottle 
(see  Appendix,  p.  354)  about  5  cm.  below  the  neck  (Fig. 
42). 

102.  Exercise.  —  Cement  a  small  porous  battery-cup  to  a 
funnel-tube  with  sealing-wax,  making  it 

air-tight  at  the  line  of  junction.  Attach 
the  diffusion-tube  to  a  two-necked  flask 
which  has  a  jet- tube  extending  through 
the  second  neck,  and  reaching  below  the 
surface  of  some  water  contained  in  the 
flask  (Fig.  43).  Fill  a  large  bell-jar 
with  hydrogen,  and  invert  it  over  the 
porous  cup.  Account  for  what  takes 
place.  Now  remove  the  jar  from  over 
the  porous  cup,  and  note  the  effect. 
Explain. 

For  method  of  preparing  hydrogen, 
consult  "  Shepard's  Chemistry,"  Exp. 
24. 

103.  Exercise.  —  Determine  the  rate  FIG.  43. 
of  diffusion  of  a  gas. 

Select  a  glass  tube  about  20  cm.  long  and  25  mm.  internal 
diameter.  By  means  of  emery-powder  and  water  on  an  old 
stove-lid  or  piece  of  flag-stone,  grind  one  end  so  that  a  glass 
plate  will  close  it  gas-tight.  Mix  plaster-of -Paris  with  water 
to  a  thin  paste,  and  out  of  it,  on  a  glass  plate,  cast  a  disk 
about  3  mm.  thick.  When  thoroughly  dry,  cut  it  with  a 
sharp  knife  to  fit  the  ground  end  of  the  tube,  cementing  it 
in  with  sealing-wax  applied  to  its  edges.  The  outer  surface 
of  the  plaster  plug  should  be  about  2  mm.  below  the  edge  of 


THE  PROPERTIES   OF  MATTER.  67 

the  tube.  Avoid  getting  any  wax  on  the  face  of  the  plug. 
Paste  a  millimetre  scale  lengthwise  of  the  tube,  having  its  zero 
at  the  inner  surface  of  the  plaster  plug,  and  give  it  a  coat  of 
thin  varnish  to  protect  it  from  water.  It  would  be  preferable 
to  etch  a  scale  on  the  glass.  (See  Art.  14.)  Over  the  closed 
end  of  the  tube,  place  a  glass  plate  coated  with  a  film  of  lard 
to  close  it  gas-tight;  then,  holding  the  open  end  of  the  tube  in 
the  water  of  the  pneumatic  trough  with  one  arm  of  a  U-shaped 
glass  tube  passing  up  within  the  tube  nearly  to  the  plug,  lower 
the  cylinder  slowly  into  the  water.  The  air  will  escape  through 
the  U-tube,  and  the  cylinder  will  be  nearly  full  of  water.  If  the 
plaster  disk  should  get  wet,  it  will  have  to  be  dried  before 
proceeding  further  with  the  experiment.  Remove  the  U-tube 
by  dropping  it  down  into  the  water- tank.  Now  take  the 
reading  of  the  water-level  in  the  tube  to  obtain  the  amount  of 
air  left  in  it.  Then,  with  a  rubber  tube,  introduce  the  gas  to 
be  examined,  filling  the  tube  down  to  the  level  of  the  water  in 
the  tank.  Take  the  reading  again ;  the  difference  of  the  two 
will  be  a  measure  of  the  amount  of  gas.  Now  remove  the 
glass  cap,  and,  as  the  water  rises  in  the  tube,  lower  the  tube  to 
keep  the  level  the  same  without  as  within  to  avoid  hydrostatic 
pressure.  When  the  water  ceases  to  rise,  take  the  reading  of 
the  water-level. 

Let  us  suppose  that  the  first  reading  was  2,  and  the  second 
100;  then  98  measures  the  amount  of  gas  introduced,  and  2 
measures  the  amount  of  air  left  in.  If  the  last  reading  taken 
was  25,  then  25  —  2,  or  23,  measures  the  air  which  passed 
through  the  porous  plug,  as  against  98,  which  measures  the 
amount  of  gas  which  passed  out  in  the  same  time.  Hence 
ff  =  4.26  is  the  ratio  of  the  diffusion  of  the  gas  under 
examination  to  that  of  air. 


68 


PRACTICAL   PHYSICS. 


104.  Exercise.  —  Determine  the  rate  of  diffusion  of  hydro- 
gen ;  also  of  oxygen. 

For  method  of  preparing  oxygen,  consult  "  Shepard's  Chem- 
istry," Exp.  7. 


105.  Exercise.  —  Tie  a  rubber  membrane 
over  the  mouth  of  a  glass  vessel  filled  with 
oxygen  gas,  and  place  it  under  a  bell-jar  filled 
with  hydrogen  gas,  standing  on  a  glass  plate. 
Account  for  what  takes  place.  Try  air  and 
common  illuminating  gas. 


106.  Exercise.  —  Fill  two  wide-mouthed  bot- 
tles with  hydrogen  and  oxygen  respectively,  having 
previously  fitted  to  them  perforated  corks  through 
which  passes  a  glass  tube  about   60    cm.  long. 
After  connecting  these  two  bottles  by  the  glass 
tube,  set  them  in  a  vertical  position  (Fig.  44), 
with  the  one  containing  the  hydrogen  uppermost.         FIG.  44. 
After  half  an  hour,  remove  the  corks,  and  apply 
a   lighted    taper.      If   a  loud   explosion   follows,   it   indicates 
that   the   gases    have    mixed.      Why    place   the   hydrogen-jar 
uppermost? 


MECHANICS   OF  SOLIDS.  69 


CHAPTER    II. 

MECHANICS     OF     SOLIDS. 
I.    LAWS    OF   MOTION. 

107.  Apparatus.  —  Wooden,  Lead,  and  Glass  Balls,  Air- 
Fump,  Spring-Balances,    Electro-Magnet,  and  certain    special 
appliances  to  be  made   in   accordance  with  directions  given 
hereafter. 

108.  Exercise.  —  Procure  two  balls  of  light  wood  of  about 
25  mm.  diameter,  place  one  of  them  near  one  end  of  a  strip  of 
common  hemp  matting  stretched  on  the  floor,  and  suspend  the 
other  by  a  string  from  some  suitable  support  so  placed  that 
the  ball  just  touches  the  one  resting  on  the  matting  at  a  point 
a  little  above  the  extremity  of  a  horizontal  diameter ;    that  is. 
the  suspended  ball  must  swing  clear  of  the  floor.     Now  pull  to 
one  side  the  suspended  ball  till  it  is,  say,  15  cm.  from  the  floor, 
and  let  it  fall  toward  the  other  ball,  striking  it,  and  setting  it 
in  motion.     Measure  the  distance  the  ball  rolls  on  the  matting 
before  stopping.     Obtain  the  average  of  several  trials. 

Repeat  the  experiment,  substituting  a  piece  of  carpet  for  the 
matting.  The  suspended  ball  must  be  raised  the  same  distance 
as  before,  in  order  that  the  force  of  the  blow  given  to  the  ball 
may  be  the  same  as  before. 

Repeat  the  experiment  on  the  floor;  also  try  as  smooth  a 
surface  as  may  be  available.  Tabulate  all  the  results. 


70 


PRACTICAL   PHYSICS. 


On  comparing  the  distances  the  ball  moves  in  the  different 
cases,  under  equal  impulses,  with  the  character  of  the  surfaces 
on  which  it  rolls,  to  what  conclusion  do  you  come?  What 
would  you  infer  would  be  the  result  if  a  surface  offering  no 
resistance  were  used? 

109.  Exercise.  —  Find  the  resultant  of  two  forces  acting 
at  an  angle  on  a  body  at  a  point. 

Procure  two  good  spring-balances  graduated  to  quarter- 
pounds,  and  a  weight  of  about  10  pounds.  Insert  screws,  at 


FIG.  45. 

Intervals  of  3  or  4  inches  in  the  frame,  about  one  of  the  upper 
corners  of  the  blackboard,  for  the  attachment  of  wires  to  which 
the  balances  are  to  be  fastened.  The  hooks  of  the  balances 
are  fastened  to  a  small  ring  to  which  is  also  attached  the  known 
weight  (Fig.  45) .  Trace  lines  of  direction  along  the  wires  with 
a  pencil.  If  accurately  drawn,  these  will  pass  through  the  centre 
of  the  ring  on  being  produced.  After  reading  the  indications  of 
the  balances,  remove  them,  extend  the  lines,  and  lay  off  on 


MECHANICS   OF  SOLIDS.  71 

them  as  many  units  of  length  as  there  are  units  of  weight 
indicated  by  the  balances  respectively.  Through  the  points 
thus  located,  draw  parallels,  making  a  parallelogram  of  which 
the  line  of  direction  of  the  weight  will  be  the  diagonal.  On 
measuring  this  diagonal,  it  will  be  found  to  be  10  units  long, 
thus  showing,  that,  if  we  represent  by  lines  the  directions  and 
the  intensities  of  two  forces  acting  at  an  angle,  the  diagonal 
of  the  parallelogram  of  which  these  lines  are  adjacent  sides 
represents  both  the  direction  and  the  intensity  of  the  result- 
ant. 

Attach  the  balances  at  different  points  in  the  frame  of  the 
board,  and  test  the  law  stated  above.  Ascertain  the  effect  of 
making  the  angle  between  the  directions  of  the  supporting  wires 
very  small.  What  do  the  balances  indicate  when  both  are 
attached  to  the  same  point,  that  is,  the  supporting  wires  are 
parallel  ?  What  does  this  show  to  be  the  value  of  the  resultant 
of  parallel  forces?  Increase  the  angle  between  the  lines  of 
direction  of  the  two  supporting  wires,  and  determine  the  effect 
on  the  readings  of  the  balances.  Make  the  angle  as  large  as 
possible.  What  would  you  infer  from  the  last  experiment 
would  be  the  effect  if  the  supporting  wires  could  be  made  to 
act  in  exactly  opposite  directions? 

110.  Exercise.  —  Procure  three  balls  of  wood  of  about 
25  mm.  diameter  each,  and  perforated  with  a  small  hole. 
Attach  each  to  a  cord  about  60  cm.  long,  and  then  suspend  the 
balls  from  a  piece  of  board  supported  in  a  clamp  by  inserting 
the  cords  through  holes  drilled  in  the  board,  the  distances 
between  them  being  such  that  each  suspended  ball  just  touches 
the  other  two.  Now  draw  off  two  of  the  balls  to  equal 
distances,  and  let  them  fall  at  the  same  instant  against  the 
ball  at  rest.  Observe  the  direction  of  its  motion.  For  one 


72  PRACTICAL   PHYSICS. 

of  the  balls,  substitute  an  iron  one  of  the  same  size,  and 
repeat  the  experiment.  Compare  the  direction  in  which  the 
third  ball  moves,  with  that  obtained  in  the  first  case.  Ascer- 
tain the  effect  of  changing  the  angle  between  the  lines 
traversed  by  the  falling  balls.  What  is  the  teaching  of  this 
experiment? 

Glass  balls  may  be  substituted  for  the  wooden  ones,  the  cord 
being  attached  to  the  ball  by  tying  it  into  a  stout  cloth 
loop  cemented  to  the  ball  by  means  of  a  pitch  cement.  See 
p.  357. 

111.  Exercise.  —  Cut  out  of  a  board  a  circular  piece  30  cm. 
in  diameter,  and  divide  it  by  radii  into  five-degree  sections 
(Fig.  46),  and  mount  it  on  a  wooden 
support.  Make  four  wooden  blocks 
of  the  form  shown  in  Fig.  47,  each 
carrying  a  pulley  about  3  cm.  in  diam- 
eter. With  small  iron  clamps,  attach 
the  four  pulleys  at  different  places 
on  the  circular  board.  Knot  together 
four  flexible  cords,  and  place  them  so 
as  to  draw  over  the  pulleys.  To  the 
free  end  of 

FIG.  46.  , 

these  cords, 

attach  weights,  adjusting  both  the 
weights  and  the  position  of  the  pul- 
leys so  that  the  knot  rests  over  the 
centre  of  the  board.  Tapping  the  ap-  FDS-  47> 

paratus  with  the  finger  will  assist  in  overcoming  friction.  The 
weights  may  be  cut  out  of  sheet  lead,  and  have  the  form  shown 
in  Fig.  48,  or  scale-pans  can  be  used,  equal  lead  balls  serving  as 
weights. 


MECHANICS   OF  SOLIDS. 


73 


FIG.  48. 


Fiu.  49. 


Now  draw  a  circle  on  a  piece  of  paper,  lay  off  on  it  the 

position  of  the  cords,  and  on  each 

line   measure  off   as  many  units  of 

distance  as  there  are  unit-weights 
attached  (Fig. 
49).  Find  by 
the  rules  given 
for  the  compo- 
sition of  forces 
the  resultant 
of  any  three  of 
the  forces  rep- 
resented, and 

compare  this  resultant  with  the  fourth  force  as  to  direction 

and  intensity.     Inference. 

Vary  the  positions   of   the  pulleys,   and  the  ratios  of   the 

weights. 

112.   Exercise.  —  Determine  the  resultant  of  two  or  more 
parallel  forces  acting  in  the 
same  direction. 

Prepare  a  rectangular  bar 
27  cm.  long,  and  having  the 
uniform  cross-section  of  1 
by  2  cm.  At  the  middle, 
and  at  intervals  3  cm.  each 
side  of  the  middle,  insert 
equal  pieces  of  brass  wire 
of  about  2  mm.  diameter 
and  3  cm.  long  (Fig.  50). 

In  each  end,  insert  a  piece  of  brass  wire  on  which  a  small 
lead  ball  screws,  to  serve  as  adjusting  weights  to  correct  for 


74  PRACTICAL  PHYSICS. 

inequalities  in  the  wooden  bar.  Construct  a  small  clevis  out  of 
brass  wire  to  be  used  as  a  support  to  the  bar.  With  common 
bullet-moulds,  cast  a  quantity  of  lead  balls.  Drill  small  holes 
through  them,  and  attach  small  wire  hooks  so  that  the  balls 
may  be  attached  to  the  bar.  or  to  each  other,  as  desired.  A 
small  pulley,  a  stout  cord  with  a  small  ring  or  scale-pan 
attached  to  one  end,  and  a  suitable  support,  will  be  needed  to 
complete  the  apparatus.  Now,  with  the  clevis,  hang  the  bar 
by  the  middle  pin,  and  counterpoise  it  over  the  pulley  by  means 
of  weights.  Move  the  adjusting  weights  till  the  bar  is  hori- 
zontal. Add  weights  at  two  points  on  opposite  sides  of  the 
clevis,  and  place  a  sufficient  number  in  the  pan  to  balance  the 
loaded  bar.  Compare  the  number  added  to  the  pan  with 
the  number  attached  to  the  bar.  Observe  the  position  of  the 
clevis,  as  well  as  the  positions  of  the  pins  to  which  the  weights 
are  attached,  and  then  frame  a  law  expressing  these  relations. 
Test  the  law  by  varying  the  positions  and  values  of  the  weights. 

A  second  device  for  determining  the  resultant  can  be  con- 
structed as  follows :  — 

Procure  a  rectangular  bar  1  metre  by  5  cm.  by  3  cm.,  of  pine, 
graduate  it  to  centimetres,  screw  on  each  end  an  ear  made  of 
sheet  brass  or  iron,  and  suspend  it  by  these  ears  in  a  horizontal 
position  from  the  hooks  of  two  spring- balances  secured  to  some 
suitable  support,  as  the  edge  of  the  laboratory  table.  Take 
the  reading  of  each  balance,  so  as  to  know  what  allowance  to 
make  for  the  weight  of  the  bar.  Now  place  on  the  bar  a 
sliding-weight  of  known  value,  sa}T  5  kg.,  and  take  the  readings 
of  the  balances  for  different  positions  of  the  weight  on  the  bar. 
Correct  the  readings  for  the  weight  of  the  bar.  Examine  the 
results  for  evidence  of  any  relation  between  the  corrected 
readings  and  the  position  of  the  weight.  Compare  the  readings 
with  the  value  of  the  weight. 


MECHANICS   OF  SOLIDS.  75 

113.  Exercise.  —  Make  two  lead   balls   of  about  3  cm. 
diameter.     To  do  this,  make  a  plaster-of-Paris   mould,  using 
a  wooden  ball  as  a  pattern. 

Suspend  them  by  cords  from 
a  horizontal  bar  so  as  just  to 
touch  (Fig.  51).  Now  draw 
one  of  them  to  one  side,  and 
let  it  fall  against  the  other. 
How  much  matter  moves 
after  the  impact,  and  how  far 
does  it  move  as  compared 
with  the  distance  the  ball 
moved  before  the  impact? 
Has  the  amount  of  motion 
been  altered  by  the  impact? 
What  has  been  changed? 
What  principles  are  sug- 
gested by  this  experiment? 

Raise  both  balls  equal  dis- 
tances in  opposite  direction,  FIG.  51. 
and    let  them   collide,   recording  the   effect.      Is  this   result 
inconsistent  with  the  laws  of  motion?     Explain. 

Bags  of    sand    can    be   used   as   substitutes   for  the  lead 
balls. 

114.  Exercise.  —  Suspend  two  elastic  balls,  ivory,  wood, 
or  glass,  by  cords,  so  as  to  swing  in  front  of  a  graduated  arc 
(Fig.  51)   for  convenience   in   comparing   distances   the   balls 
move  through.      The  balls,  when  at  rest,  should  just  touch 
each  other.     This  arc  may  be  cut  out  of  cardboard,  and  equal 
distances  measured  off  on  it  with  a  pair  of  compasses.     Raise 
one  of  the  balls  through  any  number  of  spaces,  and  let  it  fall 


76  PRACTICAL   PHYSICS 

against  the  other.  Observe  the  motion  of  the  balls  after 
impact.  Harmonize  the  result  with  the  third  law  of  motion. 
Raise  both  balls  through  equal  distances  in  opposite  directions, 
and  let  them  strike.  Explain  the  result.  Raise  one  through 
twice  the  distance  of  the  other.  Explain. 

Repeat  these  experiments  after  fastening  neatly  around  each 
ball  a  piece  of  flannel.  Explain.  Try  lead  balls.  Try  iron 
balls. 

Are  the  balls  perfectly  elastic?  What  effects  would  be 
produced  by  perfectly  elastic  balls?  What  facts  support  this 
conclusion? 

For  a  method  of  attaching  cords  to  glass  balls,  see  Art.  110. 
It  is  preferable  to  suspend  each  ball  by  two  cords,  the  ball 
forming  the  point  of  a  V,  as  the  balls  will  then  swing  in  a 
plane. 

115.  Exercise.  —  Suspend  four  or  five  highly  elastic  balls 
by  cords,  from  a  frame,  in  a  manner  similar  to  that  described 
in  Art.  114.      Raise   one   of   the   balls   through  an  observed 
distance  on  the  scale,  and  let  it  fall  against  the  adjacent  one. 
Describe  and  account  for  the  effect  produced. 

Substitute  lead  balls  for  the  ones  just  used,  or  else  cover 
them  neatly  with  flannel  or  cotton-wool,  and  repeat  the 
experiment.  Why  the  difference?  What  would  you  infer 
would  be  the  result  if  perfectly  elastic  balls  were  em- 
ployed ? 

Consecutive  balls  must  just  touch  each  other  when  at 
rest. 

116.  Exercise.  —  Cut  out  of  a  board  a  semicircular  piece 
having   a   radius    of    about   24   cm.      At  the   centre   of   the 
semicircle,    fasten    with    its    face    in    the    diameter   a   small 


MECHANICS   OF  SOLIDS. 


11 


T 


rectangular  piece  of  polished  marble.  Draw  radial  lines  divid- 
ing the  circle  into  ten-degree  spaces.  •»•»»!  i 
Suspend  from  a  wire  an  ivory  or  other 
highly  elastic  ball,  as  glass,  of  about 
2  cm.  diameter,  so  as  just  to  touch  the 
marble  surface  exactly  at  the  centre  of 
the  semicircular  board  (Fig.  52) .  Stand 
a  common  crayon  near  the  outer  end  of 
any  of  the  radial  lines ;  draw  off  the 
ball,  and  release  it  over  different  radial 
lines  till  you  find  one  by  trial  so  situ- 
ated, that,  after  the  ball  is  reflected 
from  the  marble,  it  overturns  the  crayon. 
What  law  expresses  the  relation  you  find 
existing  between  the  angles  of  incidence  and  reflection  ?  Try  a 
lead  ball.  Inference. 


FIG. 52. 


II.    CENTRE    OF   MASS.  —  STABILITY. 


117.  Apparatus.  —  Cardboard,    Round-bottomed    Flask, 
Double  Cone,  Cube,  Prism,  Pyramid,  Pulley,  etc. 

118.  Exercise.  —  Find  the  centre  of  mass  of  a  cardboard 
figure. 

Cut  a  slot  in  a  lead  bullet  with  a  knife ;  in  the  slot  place  a 
thread,  and  then  close  it  up  with  a  blow  from  a  hammer.  Cut 
from  a  sheet  of  cardboard  a  piece  of  any  desired  shape,  and 
then  suspend  it  from  the  edge  of  the  table  by  inserting  a  fine 
needle  through  the  cardboard  as  close  as  possible  to  the  edge. 
Be  sure  that  the  figure  is  free  to  turn  freely  about  the  support. 
Now  hang  the  bullet  alongside  of  this  cardboard  figure,  letting 


78 


PRACTICAL   PHYSICS. 


FIG.  53. 


the  string  press  gently  against  the  needle  (Fig.  53).  Mark 
with  a  sharp-pointed  pencil  a  point  below  the  needle,  and 
alongside  of  the  thread.  Through  this  point 
and  the  point  of  suspension,  draw  a  straight 
line.  In  the  same  manner,  locate  a  second 
line  by  suspending  the  cardboard  from  an- 
other point.  Balance  the  cardboard  figure 
on  the  point  of  a  needle  stuck  into  a  cork 
for  a  base,  and  compare  the  position  of  the 
point  when  equilibrium  is  secured  with 
the  point  of  intersection  of  the  two  lines 
drawn.  What  position  does  the  centre  of 
mass  sustain  to  the  point  of  suspension 
when  the  cardboard  hung  from  the  needle 
in  the  edge  of  the  table? 

119.  Exercise.  —  Find  the  centre  of  mass  of  the  following 
cardboard   figures :    Square,    rhombus,    rectangle,    circle,    and 
triangle.     What  simple  relation  does  this  point  sustain,  in  each 
case,  to  the  form  of  the  figure,  enabling  one  to  locate  it  by  the 
aid  of  the  ruler  alone  ? 

If  the  rectilinear  figures  are  suspended  by  their  corners,  the 
law  in  each  case  will  be  readily  seen. 

120.  Exercise.  —  Put   a   quantity   of    shot    in    a    round- 
bottomed  flask.     Then  fill  the  flask  up  with  paper  so  that  the 
shot  will  not  move  around  on  tipping  the  flask.     Now  overturn 
the  flask,  comparing  its  action  on  being  released  with  that  of 
one  not  so  loaded.      How  is  the  centre  of  mass  affected  on 
overturning  the  flask?     Where  is  the  centre  of  mass  when  the 
flask  is  at  rest? 


MECHANICS   OF  SOLIDS.  79 

121.  Exercise.  —  Thrust  a  darning-needle,  eye  first,  into  a 
large  cork,  and  try  to  make  the  apparatus  maintain  a  vertical 
position,   the  needle-point  resting  on  the  point   of   a  pencil. 
Account    for  the   failure.      Now   thrust   the 

blades    of    two    heavy-handled    knives    into 

the  cork  (Fig.  54)  on  opposite  sides,   so  as 

to    form    with    each    other    an    inverted   V. 

Ascertain   if    the   apparatus   will   now   stand 

on  the  end  of  the  pencil.     Explain.     Would 

it  answer  as  well  to  have  the  knives  perpen-  FlG-  54- 

dicular  to  the  needle  ?     Why  ?    Whenever  the  apparatus  stands 

alone,  where  is  the  centre  of  mass? 

122.  Exercise.  —  Turn  out  of  wood  a  double  cone  20  cm. 
long  and  8  cm.  in  diameter.     Make  a  V-shaped  track  (Fig.  55) 
out  of  two  thin  strips  of  board  for  the  cone  to  roll  on,  giving 
it  a  length  of  about  one  metre,  with  the  point  3  cm.  lower  than 

the  wide  end.  Now  place 
the  double  cone  at  the 
point  of  the  track,  and  it 
will  slowly  roll  toward  the 
higher  end.  Does  the  cone 
roll  up  hill?  Where  is  the 

FIG.  55. 

centre  of  mass  of  the  cone  ? 

Find,  by  measurement,  whether  the  centre  of  mass  has  been 
raised  or  lowered  by  the  motion. 

123.  Exercise.  —  Determine  the  law  governing  the  stability 
of  bodies. 

Cut  out  of  hard  wood,  the  heavier  the  better,  a  cube  1  dm. 
on  each  edge,  a  rectangular  prism  1  by  1  by  2  dm.,  and  a  right 
pyramid  whose  base  is  1  dm.  square,  and  whose  altitude  is 


80 


PEACTICAL   PHYSICS. 


2  dm.  Insert  a  small  screw-eye  in  a  face  of  each  solid  opposite 
the  centre  of  mass,  and  to  it  fasten  a  stout  flexible  cord. 
Stretch  the  cord  over  a  pulley  clamped  to  some  adjustable 
vertical  support,  attach  a  scale-pan  of  known  weight,  and  then 
add  weights  till  the  solid  begins  to  overturn.  In  this  way, 
compare  the  stability  of  these  several  solids  as  they  rest  on 
different  faces  successively,  and  generalize  a  law  from  the 
results.  The  height  of  the  pulley  should  be  such  as  to 
make  the  cord  horizontal  between  the  pulley  and  the  solid ; 
likewise,  the  base  of  the  block  must  be  secured  against 
slipping. 

III.    CURVILINEAR    MOTION. 

124.  Apparatus.  —  The  Whirling-Machine  and  its  Attach- 
ments. 

125.  Exercise.  —  Attach  to  a  whirling-machine  (Fig.  56)  a 
strong  frame,  across  which  is  stretched  a  wire  carrying  two 
equal  balls  free  to  slide  on  it,  and  connected  by  a  thread. 


FIG.  56. 


Find,  by  trial,  a  position  for  these  balls  on  the  wire,  such  that, 
when  the  apparatus  is  rapidly  rotated,  the  balls  do  not  slide 
toward  the  end  of  the  wire. 


MECHANICS   OF  SOLIDS.  81 

Repeat  the  experiment,  using  two  unequal  balls  of  known 
weights.  How  does  the  relation  of  the  weights  of  the  balls 
compare  with  that  of  their  distances  from  the  axis  of  rotation? 
What  law  of  curvilinear  motion  is  here  illustrated  ? 

126.  Exercise.  —  Determine  the  laws  for  curvilinear  motion. 

Get  a  good  mechanic  to  construct  an  attachment  for  the 
whirling-machine,  of  the  form  shown  in  the  figure  (Fig.  57),  in 
which  a  ball  is  arranged  so  as  to  be  clamped  to  a  string  which 
draws  under  a  pulley,  and  thus  lifts  a  weight  whenever  the  ball 
moves  away  from  the  centre  of  rotation.  The  weights  are  lead 
disks  of  equal  weight,  provided  with  a  slot,  so  that  they  can  be 
placed  on  the  platform  attached  to  the  cord.  The 
weight  of  this  platform  may  be  taken  as  the  unit 
weight.  The  centre  of  the  weights  must  be  exactly 
over  the  centre  of  rotation.  Let  us  suppose  that 
the  ball  is  clamped  at  20  cm.  from  the  axis,  and  a 
load  of  3  units  is  placed  on  the  platform,  making 
4  units  in  all.  Determine  the 
number  of  revolutions  the  drive- 
wheel  of  the  machine  makes  in, 

FIG.  57. 

say,  10  seconds,  in  order  just  to 

raise  the  load.  As  soon  as  the  weight  is  seen  to  lift,  then 
maintain  a  constant  speed,  and  determine  the  rate.  Use  the 
average  of  several  trials.  Now  replace  the  ball  by  one  twice 
as  heavy,  and  at  the  same  distance  from  the  axis ;  make  the 
total  load  to  be  moved  8  of  the  unit- weights,  and  find  the  speed 
necessary  to  lift  it.  The  number  of  revolutions  will  be  found 
to  be  the  same  in  each  case.  Repeat,  using  other  distances 
and  other  weights,  tabulating  the  results.  Express  as  a  law 
the  relation  between  mass  and  centripetal  force  exhibited  by 
these  experiments. 


82  PRACTICAL   PHYSICS. 

Again,  set  the  small  ball  at  8  cm.  from  the  axis,  and  deter- 
mine, as  before,  the  speed  of  the  drive- wheel  necessary  to  lift 
a  load  of  2  units.  Compare  it  with  that  necessary  to  lift  a 
load  of  4  units  when  the  ball  is  16  cm.  from  the  centre.  Also 
compare  it  with  that  necessary  to  lift  a  load  of  6  units  when 
the  ball  is  24  cm.  from  the  centre.  How  do  the  number  of 
revolutions  compare?  Express  as  a  law  the  relation  shown 
to  exist  between  the  radius  of  the  circle  traversed  by  the  ball, 
and  the  centripetal  force  or  tension  on  the  cord. 

Again,  set  the  small  ball  at  15  cm.  from  the  axis,  and 
determine  the  speed  necessary  to  lift  a  load  of  2  units. 
Compare  this  speed  with  that  required  to  lift  a  load  of  8 
units.  What  measures  the  centripetal  force  in  each  case? 
Express  as  a  law  the  relation  existing  between  speed,  or  time 
of  rotation,  and  centripetal  force. 

127.  Exercise.  —  Attach  to  the  whirling-machine  a  heavy 
ring  having  a  diameter  of  about  30  cm.  Suspend  by  a  stout 
cord  from  the  top  of  the  ring,  so  as  to  hang  in  the  axis  of 
rotation,  a  small  globe  (Fig.  58),  such  as  is 
used  for  aquariums,  in  which  has  been  placed 
some  mercury  and  some  colored  water.  Rotate 
the  apparatus,  and  observe  the  behavior  of  the 
liquids.  Explain. 

Suspend  in  a  similar  manner,  in  succession, 

Fio.  58. 

the  following  :  A  skein  of  thread,  a  loop  formed 
of  a  short  chain,  a  prolate  spheroid  of  wood,  an  oblate 
spheroid,  a  sphere,  a  double  cone,  and  a  cylinder. 

Suspend  these  geometrical  solids  from  the  extremities  of 
different  axes,  and  ascertain  if  it  makes  any  difference.  Is 
there  any  law  regulating  their  behavior  ? 


MECHANICS    OF  SOLIDS. 


83 


IV.    ACCELERATED    MOTION.  —  GRAVITATION. — 
PROJECTILES. 

128.  Apparatus.  —  Smooth    Plank,    Atwood's    Machine, 
Iron  Balls,  Electro-Magnets,  Spring-Gun,  etc. 

129.  Exercise.  —  Determine  the  laws  of  accelerated  motion. 
Take  a  straight  plank  about  5  metres  long,  and  tack  along 

the  centre  of  it  two  strips,  each  having  a  cross-section  of 
1  cm.  square,  forming  a  narrow  straight  groove  with  sharp  even 
edges  not  over  1  cm.  wide.  Graduate  one  of  these  strips  in 
centimetres.  Raise  one  end  of  the  plank  40  cm.  higher  than 
the  other  (Fig.  59). 
Suspend  a  heavy  ball 
by  a  thread  1  metre 
long,  for  a  measurer 
of  time.  With  a  little 
adjusting,  this  pendu- 
lum will  vibrate  sec- 
onds. Now  set  the 
pendulum  in  vibra- 
tion, and  at  the  instant  the  ball  reaches  the  lowest  point 
of  its  arc,  let  an  iron  ball  of  about  3  cm.  diameter  roll  down 
the  groove  on  the  plank,  starting  from  the  zero  of  the  scale 
on  the  plank.  Mark  the  point  reached  by  the  ball  at  the 
end  of  the  first  second.  Make  several  determinations  of  this 
distance.  In  like  manner,  find  the  distance  passed  over  in  2, 
3,  and  4  seconds  respectively.  What  is  the  relation  between 
the  distance  passed  over  in  successive  seconds?  How  is  the 
total  distance  passed  over  at  the  end  of  any  second  related  to 
the  number  of  that  second?  How  much  is  the  acceleration? 


Fia.  59. 


84 


PRACTICAL  PHYSICS. 


By  what  number  would  you  multiply  the  acceleration  in  this 
case  to  give  that  for  a  body  falling  freely  in  space  ?  Compare 
the  result  with  the  true  value.  Point  out  any  source  of  error 
in  the  above  method  of  determining  the  acceleration. 

A  stout  wire  stretched  tightly  across  the  room  (Fig.  60)  may 
be  substituted  for  the  plank.  A  simple  way  to  stretch  the  wire 
is  to  fasten  the  upper  end  of  it  to  the  appliance  commonly  used 
in  tightening  the  saw  in  the  ordinary  buck-saw  frame.  Place 
on  this  wire  a  pulley  carrying  a  weight  suspended  from  the 
under  side.  Parallel  to  the  wire,  and  at  a  few  centimetres 

/&\     above  it,  stretch  a  stout 
^        cord.     Pieces  of  paper 
*-•  suspended  from  this  so 

as  to  be  moved  by  the 
pulley  as  it  runs  down 
the  inclined  wire  will 
serve  to  measure  dis- 
tance. 

A  metronome,   such 
as  musicians  emplo}7  in 
measuring  time,  will  be 
found  very  serviceable  in  this  experiment. 

As  it  is  rather  difficult  to  start  the  ball  and  pendulum 
simultaneously,  it  is  recommended  to  hold  the  ball  at  the  top 
of  the  inclined  plane  by  means  of  an  electro-magnet,  with  a 
piece  of  paper  over  the  pole,  the  battery-circuit  being  closed 
by  the  iron  bob  of  the  pendulum  being  held  in  contact 
with  the  battery-poles  when  at  the  highest  point  of  its  path 
or  swing.  Then,  on  releasing  the  pendulum,  the  circuit  will 
be  broken,  and  hence  the  ball  on  the  plane  will  be  released 
at  the  same  moment.  The  electro-magnet  may  be  made 
by  winding  two  or  three  layers  of  insulated  copper  wire 


FIG.  60. 


MECHANICS   OF  SOLIDS. 


85 


No.  16,  on  a  piece  of  annealed  iron  8  cm.  long  and  2  cm.  in 
diameter. 

The  accuracy  of  the  distance  traversed  by  the  ball  can  be 
tested  by  placing  a  ruler  in  the  groove  at  the  point,  and  then 
ascertaining  if  the  click  of  the  ball  against  the  ruler  is 
coincident  with  the  expiration  of  the  time  as  indicated  by 
the  pendulum. 

130.   Exercise.  —  Determine  the  laws  of  accelerated  motion 

b}7  means  of  an  At  wood's  machine. 

A  very  efficient  Atwood's  machine  may  be  made  by  a  careful 

mechanic  as  follows  :  — 

Mount  an  accurately  balanced  metal  or  wooden  wheel  of 

20   cm.  diameter    on    the   top    of    a    heavy   wooden    column 

(Fig.  61)  set  firmly  into  a  tri- 
angular piece  of  plank,  through 
which  pass  three  wood  or  iron 
screws  to  serve  as  levelling- 
screws.  A  fine  silk  cord  passes 
over  the  wheel,  carrying  two 
weights  at  its  extremities.  On 
the  face  of  the  column,  graduate 
a  centimetre  scale  1.5  metre 
long,  with  the  zero  about  2  cm. 
below  the  lowest  point  of  the 
wheel.  Construct  out  of  brass 
or  iron  a  ring  and  a  shelf,  each 
provided  with  a  clamp,  so  that 
they  may  be  fastened  to  the 
column  at  any  desired  point  in 
the  path  traversed  by  one  of  the 

weights.      The  weights  can  be  made  of  lead  or  brass,  and 


86  PRACTICAL   PHYSICS. 

should  be  slotted  disks  of  known  weight.  The  platform  of 
one  of  the  weights  must  be  made  of  iron  in  order  that  it  may 
be  attracted  by  the  electro-magnet  placed  directly  under  it  on 
the  base.  A  metronome  or  clock  beating  half-seconds,  so 
arranged  that  it  can  be  put  in  circuit  with  a  battery  and  the 
electro-magnet,  will  be  found  very  desirable,  as  it  will  enable 
the  experimenter  to  release  the  weight  at  the  exact  beginning 
of  the  interval  of  time  marked  by  the  clock.  An  iron  ball 
suspended  by  a  cord  of  a  length  to  vibrate  half-seconds  can  be 
used  as  a  substitute,  as  in  the  last  experiment.  Slotted  bars 
of  lead  or  brass  of  known  weight,  called  "  riders  "or  "  over- 
weights," to  be  removed  by  the  ring-rest  at  any  desired  point, 
complete  the  apparatus. 

First.  Put  equal  loads  on  the  two  sides  of  the  pulley.  Set, 
by  trial,  the  ring  for  arresting  the  over-weight  so  that  the  ring- 
is  reached  by  the  descending  weight  in  one  second.  Set  the 
arresting-shelf  so  that  it  is  reached  at  the  end  of  the  second 
second.  The  lower  end  of  the  descending  weight  starts  from 
zero ;  hence  its  length  must  be  added  to  the  distance  that  the 
ring  is  below  zero,  to  give  the  distance  traversed  in  the  first 
second.  The  distance  between  the  ring  and  the  shelf  decreased 
by  the  length  of  the  weight  will  be  the  velocity  at  the  end  of 
the  first  second.  Why?  Compare  this  distance  with  that  passed 
over  in  the  first  second.  Make  several  trials. 

Secondly.  Set  the  arresting-ring  so  that  it  is  reached  by  the 
descending  weight  at  the  end  of  two  seconds.  Set  the  arrest- 
ing-shelf so  that  it  is  reached  at  the  end  of  the  third  second. 
What  is  the  velocity  at  the  end  of  the  second  second  ?  Why  ? 
After  determining,  by  repeated  trials,  the  position  of  the 
arresting-ring  and  arresting-shelf,  see  if  you  can  discover  any 
fixed  relation  between  the  velocity  at  the  end  of  any  second  of 
time  and  the  number  of  the  second. 


MECHANICS   OF  SOLIDS.  87 

Thirdly.  Place  weights  on  the  pulley  so  as  to  differ  by  some 
known  quantity ;  for  example,  use  275  grammes  and  325 
grammes,  a  difference  of  50  grammes.  Then  the  moving- force 
is  due  to  this  excess,  and  the  mass  moved  is  275  +  325  -f-  such 
a  part  of  the  mass  of  the  pulley  as,  placed  on  the  rim,  would 
be  equivalent  to  the  whole  mass  distributed  as  now  from  the 
axis  to  the  rim.  In  the  case  of  a  solid  cylindrical  pulley,  this 
quantity  is  half  of  the  total  mass  of  the  pulley.  In  the  case 
of  an  open  wheel,  it  is  approximately  the  mass  of  the  rim 
increased  by  the  mass  of  the  outer  half  of  the  spokes.  This 
can  be  found  by  computing  the  volume  in  cubic  centimetres, 
and  multiplying  it  by  the  density  of  the  substance.1  Let  the 
pulley  be  represented  by  150  grammes.  Then  the  total  mass 
moved  will  be  275  -f-  325  -f  150  =  750  grammes.  Now  deter- 
mine, by  trial,  the  position  of  the  arresting-shelf  so  that  it  is 
reached  in  one  second.  Also  determine  the  position  of  the 
arresting-shelf  when  it  is  reached  in  two  seconds.  Also  find 
the  position  when  reached  in  three  seconds.  What  is  the  ratio 
of  each  of  these  distances  to  the  first  ?  If  the  total  distance 
passed  over  is  represented  by  s,  and  the  time  by  £,  what 
formula  will  represent  the  value  of  s  in  terms  of  t? 

Fourthly.  Find,  as  in  the  last  case,  the  distance  passed  over 
by  the  descending  weight  in  one  second,  two  seconds,  three 

1  The  value  of  the  pulley  can  be  determined  experimentally  as  follows:  Let 
a  =  velocity  generated  in  unit  of  time,  w  and  w'  =  masses  attached  to  the  cord, 
w"  =  mass  of  pulley  when  considered  as  placed  at  the  circumference.  Then 

a  =  g  — w  ^"^ — .    Let  *  =  space  passed  over  by  the  descending  weight  in  t  seconds ; 
w  +  w'  +  w" 

then  s  =  — w  ~  ^ —  .  \g&.    Place  on  the  pulley  the  weights  w  and  w'.    Set  w  at  the 

w  +  w'  +  w'' 

zero  of  the  scale,  and  adjust  by  trial  the  arresting-ring  to  take  off  the  overweight 
(w  —  u/)  coincidently  with  any  subsequent  beat  of  the  clock.  The  distance  of  the 
arresting-ring  below  zero  will  be  the  value  of  *,  and  the  number  of  seconds  elapsed 
from  the  beginning  of  motion  till  the  ring  is  reached  is  the  value  of  t.  By  substituting 
these  values  in  the  formula  the  value  of  w"  can  be  determined. 


88  PRACTICAL   PHYSICS. 

seconds,  etc.  Then,  by  taking  their  difference,  we  have  the 
distance  passed  over  during  the  first  second,  second  second, 
third  second,  etc.  Find  the  ratio  that  each  of  these  distances 
sustains  to  the  first. 

131.  Exercise.  —  Determine  the  increment  of  gravity,  using 
Atwood's  machine. 

Let  us  suppose'  that  a  weight  of  275  grammes  is  placed  on 
each  side  of  the  pulley,  and  an  overweight  of  50  grammes 
on  one  side.  If  the  pulley  can  be  represented  by  150 
grammes,  then  the  mass  moved  will  equal  275  -f-  275  -f-  150 
-|-  50  =  750  grammes,  and  the  moving-force  will  be  clue  to 
50  grammes.  The  ratio  of  50  to  750  equals  the  ratio  of  the 
moving-force  to  the  force  of  gravity,  and  hence  equals  the  ratio 
of  the  velocity  the  moving-force  produces  in  a  second  to  that 

7, 

gravity  produces,  that  is,  -ff^  =  -,  in  which  k  is  twice  the 

i7 

space  the  750  grammes  move  in  one  second.  Now  determine, 
by  repeated  trials,  the  position  of  the  arresting-ring  when 
reached  in  one  second.  Hence  g  = 


132.   Exercise.  —  Find  the  measure  of  the  effect  of  a  force. 

First.  Using  an  Atwood's  machine,  put  on  one  side  of  the 
pulley,  say,  287.5  grammes,  on  the  other  312.5  grammes. 
Hence,  if  the  pulley  is  represented  by  150  grammes,  there  is 
moved  750  grammes  by  a  force  due  to  the  excess  of  25 
grammes  of  one  weight  over  the  other.  This  force  acting  on 
25  grammes  would  produce  a  velocity  of  9.8  m.  in  a  second, 
and  the  momentum  would  be  25  x  9.8  =  245.  This  force 
moves  750  grammes,  and  as  there  must  be  an  equality  of 
momenta,  then  25  x  9.8  =  750  x  velocity  acquired.  Hence 
the  velocity  acquired  by  the  750  grammes  will  be  f-JJ  =  .326, 
and  the  space  passed  over  during  the  first  second  will  be 


MECHANICS   OF  SOLIDS.  89 

o  o  /* 

-  =  .163  metre;   that  is,  if  the  arresting-shelf  is  placed  at 

2 

.163  metre  below  the  bottom  of  the  weight,  it  should  be  reached 
by  the  weight  in  one  second.  Test  it. 

Secondly.  Using  the  weights  275  grammes  and  325  grammes, 
giving  a  total  mass  of  750  grammes,  and  a  moving-force  double 
of  the  first,  being  due  to  50  grammes,  we  have  50  X  9.8 

=  750  X  velocity  acquired,  velocity  =  - — - — —  =  .653  metre, 

You 

/>  ^o 

and  space  passed  over  in  one  second  =  '-     -  =  .326  metre. 

Therefore  the  arresting-shelf  placed  at  .326  metre  should 
be  reached  in  one  second  by  the  descending  weight.  Test 
it. 

It  is  now  seen  that  a  force  due  to  50  grammes  imparts  to 
750  grammes  twice  the  velocity  that  a  force  due  to  25  grammes 
does ;  that  is,  while  the  mass  remains  constant,  the  velocity 
generated  in  a  unit  of  time  varies  as  the  force. 

Thirdly.  Keeping  the  force  which  causes  the  motion  the 
same  as  in  the  first  case,  by  putting  100  grammes  on  one  side, 
and  125  grammes  on  the  other,  making  a  total  load  of  375 
grammes,  one-half  of  the  first  load  employed,  we  have  25 
X  9.8  =  375  X  velocity  acquired,  from  which  the  velocity 

25  x  9  8 

acquired  = —  =  .653  metre,  and  the  space  passed  over 

o  /o 

=  .326  metre.     Test  it. 

Now  the  ratio  of  the  masses  moved  in  the  first  case  and  in 
the  last  is  f|f  =  2,  and  the  ratio  of  the  velocities  produced  is 

QO£ 

' =  4.     Hence,  while  the  moving-force  remains  constant, 

.653 

the  velocity  generated  in  a  unit  of  time  varies  inversely  as  the 
mass  moved.  Change  the  loads,  and  ascertain  if  this  statement 
is  general. 


90  PRACTICAL   PHYSICS. 

From  these  considerations,  it  is  evident  that  the  effect  of  a 
force  may  be  measured  by  the  product  of  the  mass  moved 
by  the  velocity  produced,  that  is,  may  be  measured  by  the 
momentum  acquired  in  a  second. 

133.  Exercise.  —  Ascertain  if  mass  affects  the  velocity  of 
falling  bodies. 

Procure  two  or  three  iron  balls  of  different  sizes,  and  as 
many  U-shaped  electro-magnets.  Tie  the  electro-magnets  to  a 
stout  stick  so  that  they  may  be  held  out  of  an  upper  window  of 
some  high  building.  These  electro-magnets  should  all  be  in 
circuit  with  a  battery  of  sufficient  strength  to  cause  them  to 
hold  up  the  balls.  By  breaking  the  circuit,  the  balls  will  all 
be  released  at  the  same  moment,  and  one  standing  on  the 
ground  can  determine  if  there  is  any  difference  of  time  in  their 
reaching  the  ground.  Does  a  difference  of  weight  perceptibly 
affect  the  time  of  falling  ? 

Drop  from  your  hand,  at  the  same  instant,  an  iron  ball 
and  a  cork  one,  and  ascertain  if  the  conclusion  in  this  case 
harmonizes  with  that  previously  reached.  Then  make  a  paper 
cone  out  of  light  cardboard,  and  of  sufficient  size  to  hold  both 
balls.  After  placing  the  balls  in  the  cone,  the  iron  one  first, 
drop  it  point  first.  Are  the  results  the  same  as  before? 
Explain. 

Drop  a  coin  and  a  paper  disk  of  the  same  size  simultaneously, 
comparing  the  result  with  that  obtained  by  placing  the  paper 
disk  on  top  of  the  coin,  and  dropping  them  from  the  hand. 
Now  place  the  coin  and  the  paper  disk  in  a  long  glass  tube 
sealed  at  one  end,  and  having  a  stop-cock  fitted  to  the  other. 
Such  an  apparatus  is  supplied  by  dealers  under  the  name  of 
Guinea  and  Feather  Tube.  Connect  the  tube  with  the  air- 
pump,  and  exhaust  the  air  as  perfectly  as  possible.  Close 


MECHANICS   OF  SOLIDS.  91 

off  the  tube,  remove  it  from  the  pump,  invert  quickly,  and 
ascertain  if  the  relative  time  of  falling  of  the  two  objects  is 
affected  in  any  way. 

Prepare  a  set  of  propositions  embodying  the  truths  exhibited 
by  these  experiments. 

134.  Exercise.  —  Support  a  pail  of  water  at  an  elevation 
of  two  or  more  metres  above  the  floor.     Place  in  the  pail  one 
end  of  a  rubber  tube  of  sufficient  length  to  reach  to  the  floor. 
In  the  other  end  of  the  tube,  insert  a  short  piece  of  glass  tubing 
drawn  out  to  a  jet-point.     See  p.  356.      Secure  this  tube  in  the 
jaws  of  a  suitable  clamp  so  that  any  desirable  direction  may 
be  given  to  it.     Start  the  water  flowing  through  the  tube  by 
suction,  and  then  observe  the  shape  of  the  path  of  the  stream, 
and  the  horizontal  distance  reached  by  it,  as  the  direction  of 
the  jet-tube  is  changed.     Inference.     Ascertain  the  effect  of  a 
change  in  the  height  of  the  pail  above  the  end  of  the  jet-tube. 
What  forces  determine  the  path  of  the  stream  ? 

135.  Exercise.  —  Determine  the  path  of  a  projectile. 
Construct  a  spring-gun  after  the  pattern  shown  in  Fig.  62. 

The  horizontal  and  vertical  pieces  are  2.5  cm.  thick ;  N  is  a 
cylinder  with  tenons  of  equal  length  sliding  freely  through 
round  holes  in  the  vertical  pieces  ;  K  is  a  pin  to  serve  as  a 
handle  ;  L  and  M  are  elastics  or  spiral  springs  firmly  fastened 
to  N  and  the  vertical  CD.  Two  wooden  balls  of  the  same 
diameter  are  needed.  Through  each,  drill  a  hole  of  such  a  size 
that  either  will  slide  easily  on  the  tenon  F.  The  tenons  on  N 
should  be  of  such  a  length,  that,  when  N  is  drawn  back,  the 
right-hand  one  will  be  flush  with  the  face  of  CD,  and  the  left- 
hand  one  will  project  a  distance  equal  to  the  diameter  of  the 
ball.  Now  draw  N  back,  place  one  ball  on  F,  and  the  other 


92  PRACTICAL  PHYSICS. 

on  the  ledge  CB  opposite  the  hole  at  H  ;  then  release  N,  and 
it  will  be  seen  that  both  balls  will  be  set  in  motion  at  the  same 
time,  one  falling  vertically,  and  the  other  moving  as  a  projectile. 
AB  must  be  held  in  a  horizontal  position.  Compare  the  mo- 
tions of  these  balls,  and  the  times  required  to  reach  the  floor. 

To  picture  the  path  of  the  projectile,  hold  the  spring-gun  so 
that  the  path  of  the  ball  will  be  parallel  to  a  vertical  wall,  and 
distant  a  few  centimetres  from  it.  By  watching  carefully  the 

ball,  it  will  be  found 
possible  to  insert  a 
pin  in  the  wall  op- 
posite some  position 
of  the  ball  in  its 
flight,  new  points 
being  marked  each 
FIG.  62.  *  trial,  as  well  as 

those    just    located 

verified.  A  line  traced  through  these  points  will  represent 
closely  the  path  of  the  projectile.  This  can  be  transferred  to  a 
sheet  of  paper  by  ascertaining,  first,  the  vertical  distance  of 
each  of  these  points  from  the  horizontal  line  passing  through 
the  highest  point  of  the  curve,  as  well  as  the  horizontal 
distance  from  the  initial  point  of  the  curve ;  and  secondly, 
locating  them  with  reference  to  a  corresponding  line  drawn 
on  a  sheet  of  paper,  reducing  each  measurement  on  the  same 
scale. 

V.  THE  PENDULUM. 

136.  Apparatus.  —  A   number   of   Balls    to   use   in   con- 
structing pendulums. 

137.  Exercise.  —  Determine  the  laws  for  the  vibrations  of 
pendulums. 


MECHANICS   OF  SOLIDS. 


93 


Fasten  to  each  of  a  number  of  lead  balls,  of  about  15  mm. 
diameter,  a  stout  cotton  thread,  by  cutting  in  each  a  slot  with 
a  knife,  inserting  one  end  of  the  thread,  and  closing  it  up  by  a 
blow  from  a  hammer.  Drill  a  number  of  holes,  5  cm.  apart, 
through  a  piece  of  board  about  60  cm.  long,  5  cm.  wide,  and 
15  mm.  thick.  Pass  the  strings  through  these  holes,  securing 
each  in  its  place  with  a  small 
wooden  wedge.  Support  this 
board  in  a  horizontal  position 
in  some  suitable  way  (Fig.  63). 
These  suspended  balls  will  serve 
as  pendulums,  the  lengths  being 
the  distances  respectively  from 
the  under  side  of  the  support 
to  the  centre  of  the  balls,  and 
easily  varied  by  pulling  the  strings 
through  the  holes  in  the  support. 
Marbles  may  be  substituted  for 
the  lead  balls,  the  strings  being 
attached  by  some  very  adhesive 
cement.  See  p.  357. 

First.  -Set  one  of  these  pendulums  swinging  through  a  small 
arc,  about  five  degrees,  and  determine  the  number  of  vibrations 
made  in  thirty  seconds  by  averaging  several  trials.  Now  set 
the  pendulum  vibrating  through  a  much  larger  arc,  and  deter- 
mine the  number  of  vibrations  made  in  thirty  seconds.  Does 
the  size  of  the  arc  affect  the  time?  Test  the  conclusion  by 
extending  the  time  of  observation,  as  well  as  increasing  still 
more  the  size  of  the  arc. 

Secondly.  Adjust,  by  trial,  the  length  of  one  of  the  pendu- 
lums so  that  its  time  of  vibration  is  one  second.  How  long  is 
the  pendulum?  Adjust  another  to  vibrate  in  half-seconds; 


FIG.  63. 


94  PBACTICAL  PHYSICS. 

another  in  one-third  of  a  second.  Compare  the  lengths  of 
these  several  pendulums,  ascertaining  if  there  is  any  simple  law 
connecting  the  lengths  of  the  pendulums  with  their  times  of 
vibration. 

Thirdly.  Set  up  two  pendulums  of  the  same  length,  using  a 
wooden  ball  for  the  bob  of  one,  and  a  metal  ball  for  the  other. 
Compare  carefully  their  times  of  vibration.  Inference. 

Fourthly.  Using  an  iron  ball  as  a  bob  for  a  pendulum, 
determine  carefully  its  time  of  vibration.  Now  place  just 
below  the  lowest  point  traversed  by  the  ball,  a  pole  of  an 
electro-magnet,  and  again  determine  the  time  of  vibration. 
Would  you  infer  from  the  comparison  of  these  times,  that  an 
increase  in  the  force  of  gravity  would  affect  the  time  of 
vibration  of  a  pendulum? 

138.  Exercise.  —  Fasten  six  lead  or  iron  balls  on  a  stout 
string  at  intervals  of  15  cm.,  forming  a  compound  pendulum 
about    105    cm.  long.      Set   the   pendulum   in   vibration,   and 
determine  its  time.     Find  the  time  of  vibration  of  a  pendulum 
whose  length  is  the  distance  of  the  centre  of  the  lowest  ball 
of  the  six  from  the  point  of  support.     In  like  manner,  find  the 
times  of  pendulums  whose  lengths  are  the  distances  respectively 
of  the  other  balls  from  the  point  of  support.     Set  up  a  pendu- 
lum whose  time  is  that  of  the  compound  pendulum.      Notice 
the  shape   of   the   compound  pendulum  when  vibrating,   and 
apply  the  facts  ascertained  above  to  account  for  it.      Which 
ball  would   you   remove   to  shorten   the   time,   and  which  to 
lengthen?     Add  another  ball  to  the  number  without  affecting 
the  time.     Explain. 

139.  Exercise.  —  Suspend  from  a  suitable  frame  a  uniform 
strip  of  wood  about  1  metre  long,  5  cm.  wide,  and  1  cm.  thick, 


MECHANICS   OF  SOLIDS. 


95 


by  driving  into  the  end  of  it  a  small  wire  staple,  forming  an 
eye  through  which  a  knitting-needle  can  be  passed  to  serve  as 
an  axis  of  oscillation  (Fig.  64) .  Adjust  a  pendulum,  as  in  the 
last  experiment,  to 
vibrate  in  the  same 
time  as  the  wooden 
bar.  Compare  the 
length  of  the  pen- 
dulum with  that  of 
the  bar.  Now  cut 
from  a  sheet  of  lead 
a  piece  weighing 
half  a  kilogramme. 
Bend  this  into  a 
clasp  that  will  slide 
along  the  bar  with 
sufficient  friction  to 

stay  wherever  placed.  Having  measured  off  on  the  bar  the 
length  of  the  pendulum  vibrating  in  the  same  time,  place  the 
sliding-clasp  below  that  point  on  the  bar,  and  note  the  effect 
on  its  time  of  vibration.  Note  the  effect  when  the  weight  is 
at  the  point,  and  also  when  above  the  point. 

140.  Exercise.  —  Suspend  a  wooden  bar  as  in  the  last 
experiment,  and  adjust  a  pendulum  to  vibrate  in  the  same 
time.  Bore  a  hole  through  the  wooden  strip  at  the  point 
marked  in  that  experiment,  and  support  the  bar  by  passing 
the  needle  through  it.  How  does  its  time  of  vibration 
compare  with  its  previous  time?  State  as  a  proposition  the 
relation  found  to  exist  between  this  point  and  the  centre  of 
suspension. 


FIG.  64. 


96  PRACTICAL  PHYSICS. 

141.  Exercise.  —  Suspend  a  common  lath  by  a  cord  10  or 
15  cm.  longxso  as  to  swing  as  a  pendulum.     Adjust  a  ball- 
pendulum  to  vibrate  in  the  same  time.     Mark  a  point  on  the 
lath  distant  from  the  suspension-point  the  length  of  the  ball- 
pendulum.     Now  set  the  lath  in  vibration  by  striking  it  with 
a  ruler  opposite   this   point.      Compare   the  effect  with   that 
produced  when  the  lath  is  put  in  vibration  by  a  blow  delivered 
at  some  other  point  on  the  bar.     Inference. 

VI.    FRICTION. 

142.  Exercise.  —  Measure  the  friction  between  two  surfaces 
when  one  moves  over  the  other. 

Procure  a  board  about  1  metre  long  and  25  cm.  wide,  dressed 
to  a  plane,  and  a  rectangular  block  12  x  6  x  4  cm.  In  the 
centre  of  each  of  any  three  faces  about  a  corner,  insert  a  screw- 
eye  for  convenience  in  attaching  a  cord.  Weigh  the  block, 
place  on  it  any  convenient  number  of  grammes,  attach  a 
spring-balance  by  means  of  a  cord ;  then,  keeping  the  cord 
horizontal,  apply  sufficient  force  to  move  the  block,  reading  the 
balance  just  as  the  block  starts  to  move,  and  also  after  motion 
has  begun.  Make  several  determinations  of  both  the  starting 
and  the  moving  force. 

Repeat  the  tests  to  ascertain  if  the  area  of  the  face  of  the 
block  resting  on  the  board  affects  the  results. 

Ascertain  the  effect  of  using  a  greater  weight. 

Determine  the  effect  of  varying  the  character  of  the  sub- 
stances by  placing  a  plate  of  glass,  iron,  brass,  etc.,  on  the 
board,  and  cementing  to  the  face  of  the  block  a  thin  sheet  or 
plate  of  the  same  substance. 

Measure  the  friction  between  the  surfaces  when  coated  with 
some  kind  of  lubricator. 


MECHANICS   OF  SOLIDS. 


97 


Make  several  determinations  in  each  case,  and,  using  the 
mean  as  the  most  probable  value  of  the  force  applied,  divide 
it  by  the  mass  moved,  to  obtain  the  coefficient  of  friction. 

As  a  substitute  for  the  balance,  the  string  may  be  stretched 
over  a  pulley  by  weights  placed  in  a  scale-pan. 


VII.    THE    SIMPLE   MACHINES. 

143.  Apparatus.  —  A   Lever,    several   Pulleys,    a   Wheel 
and  Axle,  an  Inclined  Plane,  and  a  Set  of  Weights. 

144.  Exercise.  —  Determine  the  law  of  equilibrium  for  the 
lever. 


The  apparatus  employed 
in  Art.  112  will  be  found 
useful  for  this  one.  When 
any  other  point  than  the 
centre  of  the  bar  is  taken 
as  the  fulcrum,  the  weight 
of  the  bar  can  be  neutral- 
ized by  means  of  a  lead 
ball  made  to  screw  on  the 
end  of  the  wire  inserted  in 
the  end  of  the  bar.  A  Y- 
shaped  support  (Fig.  65) 

will  be  found  convenient,  but  it  is  not  indispensable,  as  the 

wire  clevis  can  be  used  to  support  the  bar. 


PIG.  65. 


98 


PRACTICAL  PHYSICS. 


Set  the  fulcrum  at  any  point,  and  counterpoise  the  bar. 
Suspend  any  number  of  weights  from  a  point  on  one  side  of 
the  fulcrum,  and  a  sufficient  number  from  a  point  on  the 
opposite  side  to  cause  the  bar  to  assume  a  horizontal  position. 
Compare  the  ratio  of  these  weights  with  that  of  the  spaces 
between  their  points  of  attachment  and  the  fulcrum.  Vary  the 
weights  and  their  points  of  attachment.  Arrange  the  apparatus 
so  that  one  weight  is  between  the  fulcrum  and  point  of  appli- 
cation of  the  other  weight.  What  law  do  you  find  expresses 
the  relation  between  the  weights  and  the  arms  of  the  lever  ? 

145.  Exercise.  —  Secure  in  a  vertical  position  a  board 
about  1  metre  long  and  40  cm.  wide.  Mount  on  this  board  a 

circular  wooden  disk  of  about  20 
cm.  diameter,  so  that  it  can  turn 
freely  about  a  fixed  axis  through 
the  centre.  Attach  at  any  two 
points  of  the  disk  cords  which 
pass  over  pulleys  (Fig.  66)  which 
can  be  given  any  desired  position 
on  the  supporting  board  by  hav- 
ing, as  their  axes,  bolts  moving 
in  vertical  slots,  and  fastened  by 
nuts.  To  the  ends  of  these 
cords,  attach  scale-pans  cut  out 
of  tin  plate.  Now  place  known 
weights  in  these  pans,  and  when 
the  apparatus  assumes  a  position 
of  rest,  measure  the  perpendicular 

distance  from  the  centre  of  the  disk  to  the  line  of  direction  of 
each  cord,  and  compare  their  ratio  with  that  of  the  weights. 
The  weights  should  include  the  pans,  and  the  position  of  the 


FIG.  66. 


MECHANICS   OF  SOLIDS. 


99 


cords  should  be  such  that  the  direction  does  not  pass  through 
the  centre  of  the  disk.  Make  a  number  of  experiments  in 
which  the  weights  and  the  positions  of  the  pulleys  are  changed. 
Express  as  a  law  the  relation  found  to  exist. 

146.  Exercise.  —  Determine    the    law    for   the    movable 
pulley. 

With  three  small  pulleys,  some 
flexible  cord,  and  two  small  scale- 
pans,  set  up  successively  the 
arrangements  shown  in  Fig.  67. 
Place  shot  in  one  of  the  pans  to 
counterbalance  the  weight  of  the 
pulleys,  then  place  known  weights 
in  the  two  pans,  and  ascertain 
the  ratio  between  them  whenever 
equilibrium  is  secured.  Account 
for  the  value  of  the  ratio  in  each 
case. 

FIG.  67. 

147.  Exercise.  —  Determine  the  law  of  equilibrium  for  the 

wheel  and  axle. 

A  suitable  apparatus  for 
this  experiment  may  be  made 
by  a  good  mechanic  as  fol- 
lows :  — 

Procure  a  piece  of  hard  wood  about  15 
cm.  long,  and  of  about  the  same  diameter. 
Turn  it  down  in  a  lathe  so  as  to  have  a 
succession  of  disks  with  diameters  as  the 
numbers  1,  2,  3,  etc.     These  disks  need  not  be  more  than  2.5 
cm.  thick.     Fasten  to  the  circumference  of  each  disk  a  cord  for 


FIG.  68. 


100  PRACTICAL   PHYSICS. 

the  attachment  of  weights.  The  axis,  consisting  of  a  piece  of 
brass  or  iron  rod  driven  into  the  ends  of  the  piece  of  timber, 
can  be  supported  from  two  brackets  firmly  screwed  to  the  edge 
of  a  piece  of  plank  (Fig.  68) .  Attach  scale-pans  to  the  cords  ; 
place  shot  in  one  till  equilibrium  is  secured,  then,  employing 
known  weights  in  the  pans,  ascertain  the  law  of  the  machine. 

148.     Exercise.  —  Determine    the    law    for   the    inclined 
plane. 

Construct  an  apparatus  for  this  experiment  as  follows :  — 

Hinge  together  two  pieces  of  board,  each  about  15  cm.  wide 

and  50  cm.  long.     On  the  under  side  of  the  one  to  be  used  as 

the  inclined  plane,  fasten  thin  strips  across  it  at  intervals  of 

2  cm.     Then,  by  means  of  a  prop  moved  along  between  the 

boards,  kept   from   slipping   by 
the  strips  on  the  upper  one,  any 
desired  elevation  may  be  given 
FIG  69  to  the  plane.    Fasten  a  pulley  at 

the  opposite  end  from  the  hinge, 

so  that  a  cord  attached  to  a  car  moving  along  the  plane,  and 
drawing  over  the  pulley,  will  be  parallel  to  the  plane.  Place 
weights  in  the  scale-pan  to  counterpoise  the  car,  then  add  weights 
to  both  the  car  and  the  scale-pan,  comparing  them,  when  equi- 
librium is  secured,  with  the  dimensions  of  the  plane. 
Fig.  69  illustrates  a  modified  form  of  this  apparatus. 


MECHANICS   OF 


CHAPTER    III. 


MECHANICS     OF     FLUIDS. 


[.    PRESSURE    IN    FLUIDS. 


149.  Apparatus.  —  Large    Glass    Tube,    Two-litre    Bottle, 
Metal  Tube,   Bladder-Glass,   Weight-Lifter,  Magdeburg  Hemi- 
spheres,   Air-Pump,    Glass    Tubing,    Barometer-Tube,    Aneroid 
Barometer,  small   Rubber  Foot-Ball,  Glass   Bolt-Head,  Model 
of  Sprengel  Pump,  etc. 

150.  Exercise.  —  Close  with  a  cork  one 
end  of  a  brass  or  tin  tube  about  1  metre 
long    and   3    cm.  in    diameter,    and   set  it 
into  a  wooden  block  for  a  base.      In  the 
side   of   the   tube,   drill   five   holes  5  mm. 
in  diameter,  at  equal  distances  apart,  and 
placed    so    that    the   third    hole   is   at   the 
middle  of  the  tube  (Fig.  70).     Close  these 
apertures  with  corks,  and  fill  the  tube  with 
water.     On  uncorking  the  apertures,  com- 
pare the  ranges  of  the  streams,  and  also 
ascertain  if  they  differ  in  force.     Inference. 
The  water  in  the  tube  should  be  kept  at  a 

constant   level  while   these   comparisons  are  being  made,   by 
pouring  water  from  a  suitable  vessel. 


FIG.  70. 


102 


PRACTICAL   PHYSICS. 


151.  Exercise.  —  Ascertain    if     the    atmosphere    exerts 
pressure. 

Tie  firmly  a  piece  of  sheet-rubber  over  one  end  of  a  large 
tube,  tin  or  glass,  about  30  cm.  long  and  5  cm.  in  diameter. 
After  filling  it  with  water,  invert  it  in  a  vessel  of  water, 
keeping  the  mouth  just  below  the  surface.  Observe  the  shape 
of  the  rubber  surface.  Ascertain  the  cause  of  it  by  substituting 
a  carefully  fitted  glass  plate  for  the  rubber,  and  comparing  the 
force  needed  to  pull  it  off  when  the  tube  is  full  of  water  with 
that  when  free  from  water. 

152.  Exercise.  —  Tie   a  piece   of   sheet-rubber  or  tough 
paper  over  one  end  of  a  bladder-glass,  place  it  on  the  table 
of  the  air-pump,  and  exhaust  the  air.     What  fact  is  proved? 

To  make  a  bladder-glass,  cut  off  the  bottom  of  a  common 
glass  fruit-jar  (see  p.  354),  and  grind  down  the  edges  on  a 
piece  of  flat  sandstone.  g=s» 

Coat   with   lard   the   edges   of    the   glass 
resting  on  the  air-pump  table. 

153.  Exercise.  —  Connect  the  Weight- 
Lifter  (Fig.  71)  to  the  air-pump  by  a  piece 
of  heavy  rubber  tubing.      Account  for  the 
upward   movement   of   the   piston  with   the 
heavy   weight    attached    as    the    air   is    ex- 
hausted  from   the   cylinder.      Measure    the 
cylinder,  and  compute  how  great  a  weight 
can  be  lifted  by  the  machine.     Remove  the 
piston,  and  tie  a  rubber  membrane  across 

the  end  of  the  cylinder.  Observe  the  effect  on  the  membrane 
on  exhausting  the  air  as  different  positions  are  given  to  the 
cylinder,  varying  from  vertical  to  horizontal.  Inference. 


Fm.  71. 


MECHANICS  OF  FLUIDS. 


103 


154.  Exercise.  —  Connect   the   Magdeburg   Hemispheres 
(Fig.  72)  with  the  air-pump.     Exhaust  the  air,  remove  them 

from  the  pump,  and  then  try  to  separate  them. 
While  thus  fastened  together,  place  them  under 
a  bell- jar  on  the  table  of  the  air-pump,  exhaust 
the  air,  and  observe  the  effect.  What  do  yon 
find  held  the  hemispheres  together?  Ascertain 
if  the  hemispheres  can  be  pulled  apart  in  any 
one  position  more  easily  than  in  another.  In- 
FIG.  72.  ference. 

155.  Exercise.  —  Compare    the 
pressure  exerted  by  fluids  in  different 
directions. 

Bend  a  stout  glass  tube  about  75 
cm.  long  into  the  form  shown  in 
Fig.  73  (a),  and  also  three  shorter 
pieces  into  the  forms  shown  in  (b), 
(c),  and  (d).  In  the  U-shaped  part 
of  (a),  pour  enough  mercury  to  rise 
about  1  cm.  in  each  arm.  Attach 
the  tube  (b)  to  the  lower  end  of  (a) 
with  a  rubber  connector,  and  hold  the 
apparatus  vertically  in  a  vessel  of 
water,  observing  the  distance  of  the 
mouth  of  (b)  below  the  surface  of 
the  water,  and  also  the  effect  on  the 
level  of  the  mercury  in  (a).  Now 
substitute  the  tube  (c)  for  (b),  sub- 
merging the  apparatus  to  the  same  depth  as  before,  as 
indicated  by  the  mouth  of  the  tube.  Note  the  change  in 
the  mercury  level.  Try  (d).  What  causes  the  change  of 


FIG.  7 


104  PRACTICAL  PHYSICS. 

level?      What   is   the   evidence?      What   truth   is   proved   by 
this  experiment? 

The  tubes  (b),  (c),  and  (d)  must  be  filled  with  water  as 
high  as  the  mouth,  to  insure  success. 

156.  Exercise.  —  Cut  a  board  about  75  cm.  long,  15  cm. 
wide,  and  15  mm.  thick.     Place  it  on  a  table  so  that  it  projects 
25  cm.  over  the  edge.     Spread  a  large  newspaper  over  the  end 
on  the  table,  making  it  as  smooth  as  possible.     Now  strike  the 
projecting  part  of  the  board  with  the  hand,  comparing  the  blow 
necessary  to  raise  the  other  end  of  the  board  with  that  required 
when    the    paper   is    removed,    or   a    smaller   paper   is    used. 
Explain. 

157.  Exercise.  —  Select    two    test-tubes,    such   that   one 
slides  easily  within  the  other.     Fill  the  larger  one  with  water, 
insert  the  closed  end  of  the  smaller  tube,  and  quickly  invert. 
Account  for  the  upward  movement  of  the  small  tube  in  opposi- 
tion to  the  force  of  gravity.     What  is  the  office  of  the  water  in 
this  experiment? 

158.  Exercise.  —  Measure  the  atmospheric  pressure. 

Fill  a  heavy  glass  tube  about  80  cm.  long,  and  closed  at  one 
end,  with  mercury.  To  do  this,  connect  to  the  tube  a  small 
glass  funnel  by  means  of  a  rubber  connector.  Invert  it  in  a 
cup  of  mercury  (Fig.  74)  by  placing  the  finger  firmly  over  the 
end  of  the  tube  to  keep  the  mercury  from  running  out  during 
the  operation.  Why  does  not  the  mercury  all  run  out  of  the 
tube?  Devise  some  way  of  showing  that  it  is  atmospheric 
pressure  on  the  mercury  in  the  cup  that  supports  the  column 
in  the  tube.  Measure  the  height  of  the  column  m  the  tube 
above  the  level  of  the  mercury  in  the  cup.  Incline  the 


MECHANICS   OF  FLUIDS. 


105 


tube,    and   again   determine   the    difference    of    level.      Why 
the  same? 

Measure  the  cross-section  of  the  tube,  and  then  compute  the 
volume  of  mercury  in  cubic  centimetres. 
Multiply  this  volume  by  13.6,  and  you 
have  the  weight  of  mercury  in  grammes. 
Compute  what  the  weight  would  be  if  the 
cross-section  of  the  tube  were  1  scm., 
and  the  mercury  column  76  cm.  long. 

In  filling  the  tube  with  mercury,  re- 
move air-bubbles  by  sliding  down  the 
tube  a  slender  iron  wire. 

159.  Exercise.  —  Measure  the  height 

of   a   building  or  hill  by   means  of   a 

barometer. 

For   this    purpose,    use   an   Aneroid 

Barometer    (Fig.   75),    as    it    is   more 

portable  and 

more     sen  si-  FlG- 74> 

tive  than  the  mercurial.  Note  the 
rise  or  fall  of  the  barometer  in  hun- 
dredths  of  an  inch  in  passing  from 
one  station  to  the  other,  multiply  by 
9,  and  the  product  is  the  difference 
in  altitude  expressed  in  feet.  If  the 
pressure  is  below  26  inches,  or  the 
temperature  above  70°  F.,  use  10  for 
a  multiplier.  Many  readings  at  both 
stations  should  be  taken,  extending 

over  a  period  of  several  days,  the  averages  being  used  in  the 

computation. 


FIG.  75. 


106 


PRACTICAL  PHYSICS. 


The  readings  should  be  taken  with  the  aneroid  in  a  horizontal 
position,  tapping  the  face  slightly  with  the  finger  before  taking 
them  in  order  to  bring  the  needle  into  equilibrium.  Guard 
against  parallax  in  taking  the  readings,  and  estimate  all 
fractions  of  spaces. 

For  more  accurate  methods  of  measuring  heights,  consult 
Plympton's  "Aneroid  Barometer,"  published  by  D.  Van 
Nostrand,  New  York. 

160.  Exercise.  —  Fill  a  small  rubber  foot- 
ball  half   full   of   air,   and   place   it  under  a 
bell-jar  on  the  air-pump  table.     Exhaust  the 
air  from  the  jar ;  notice  the  effect  on  the  ball. 
Explain. 

Substitute  a  dish  of  soap-bubbles  for  the 
ball,  or  an  empty  bottle  with  its  mouth  opening 
under  water  in  a  tumbler. 

What  property  of  air  do  these  experiments 
show? 

161.  Exercise.  —  Procure  a  bolt-head,  that 
is,  a  stout  glass  tube  with  a  large  bulb  on  one 
end.     A  strong  glass  tube  fitted  air-tight  to 
a  bottle  by  means  of  a  perforated  cork  will 
make  a  good  substitute.     Close  the  top  of  an 
open-top  bell-jar  with  a  good  cork,  through  FIG.  76. 
which  passes  this  glass  tube  reaching  to  the 

bottom  of  a  vessel  of  water  within  it  (Fig.  76).  Place  the 
apparatus  on  the  table  of  an  air-pump,  exhaust  the  air,  and 
watch  the  effect.  Also  observe  the  effect  of  admitting  the  air. 
Explain. 


MECHANICS   OF  FLUIDS. 


107 


162.  Exercise.  —  Fit  to  a  flask  or  bottle  a  good   cork, 
through  which  passes   a   jet-tube.      Connect  this  tube  to  an 
air-pump  by  means  of  a  rubber  tube,  and  exhaust  the  air. 
Close  the  connection  between  the  flask  and  the  pump  with  a 
pinch-cock,   disconnect   the   tube   from   the    pump,   and   open 
the  pinch-cock  after  placing  the  mouth  of  the  rubber  tube  in 
a  vessel  of  water.     Explain. 

163.  Exercise.  —  Connect  with  rubber  tubing,  as  shown  in 
Fig.  77,  a  glass  funnel,  a  T-tube,  a  stout  glass  tube  one  metre 
long,  and  a  flask  to  be  exhausted. 

On  the  rubber  connector,  between' 
the  T-tube  and  the  funnel,  place 
an  adjustable  pinch-cock.  Secure 
the  apparatus  in  a  vertical  position, 
with  the  lower  end  of  the  tube 
fitting  into  a  vessel  which  has  an 
opening  on  the  side  a  little  higher 
than  the  end  of  the  tube.  Now 
close  the  pinch-cock,  pour  mercury 
into  the  funnel,  and  open  the  pinch- 
cock  on  the  tube  leading  to  the 
vessel  to  be  exhausted.  Then  open 
the  pinch-cock  so  that  the  mercury 
falls  in  a  rapid  series  of  drops, 
closing  the  tube,  and  preventing, 
air  from  entering  from  below.  As 
the  mercury  flows  down,  the  ex- 
haustion begins,  the  air  of  the  tube  being  carried  down  by  the 
mercury  drops,  and  the  air  of  the  flask  expanding  to  fill  its 
place.  The  mercury  can  be  poured  back  into  the  funnel  from 
time  to  time,  care  being  exercised  to  prevent  the  funnel's 


FIG.  77. 


108  PRACTICAL   PHYSICS. 

becoming  empty,  as  then  air  would  immediately  enter  the  flask. 
Search  for  evidence  in  the  working  of  this  mercury-pump, 
showing  that  the  degree  of  vacuum  is  improving. 


II.    LAW    OF   BOYLE. 

164.  Apparatus.  —  Heavy  Glass  Tubing,  Mercury,  etc. 

165.  Exercise.  —  Determine  the  law  of  the  compressibility 
of  gases. 

First.  Close  one  end  of  a  stout  glass  tube  in  a  gas-flame, 
and  then  bend  it  into  the  shape  of  the  letter  J,  the  short 
arm  bsing  the  closed  one,  and  about  25  cm.  long  (Fig.  78). 
Lengthen  the  long  arm  to  2  metres,  using  a  heavy  rubber 
connector,  and  winding  it  with  fine  copper  wire.  Fasten  the 
completed  tube  with  metal  straps  to  a  board  set  into  a  block 
for  a  base.  Attach  metric  scales  to  the  arms,  placing  the  zero 
of  each  one  on  the  same  level,  and  just  above  the  bend  in  the 
tube.  Now  pour  in  enough  mercury  just  to  close  the  bend  up 
to  the  zero  of  the  scales,  bringing  the  mercury  to  the  same 
level  by  jarring  the  tube.  Under  what  pressure  is  the  air  in 
the  short  arm  ?  After  this  adjusting  has  been  carefully  done, 
pour  in  mercury  till  a  reading  of  about  20  cm.  is  secured  in  the 
long  arm.  Record  the  height  of  the  mercury  column  in  each 
arm.  Add  more  mercury  and  record  the  readings,  proceeding 
in  this  way  till  the  long  arm  is  full  of  mercury.  The  difference 
of  any  two  corresponding  readings,  plus  the  barometer  reading 
at  the  time  of  conducting  the  experiment,  will  measure  the  pres- 
sure on  the  confined  air-column.  Why  ?  Compute  the  pressure 
for  each  observation  and  multiply  it  by  the  length  of  the  con- 
fined air-column  corresponding  to  it.  If  the  experiment  is  care- 
fully conducted  these  products  will  be  found  to  be  nearly  equal. 


MECHANICS   OF  FLUIDS. 


109 


Tabulate  the  results. 

Express  as  a  law  the  relation  between  volume  and  pressure 
exhibited  by  the  experiment.  Represent  this  relation  by  a 
curve  (598). 

The  mercury  must  be  poured  in  the  tube  very  gently,  and 
with  the  tube  in  an  inclined  position  at  first,  so  that  the  mercury 
stream  will  not  act  as  a  piston,  and  drive  air 
ahead  of  it  into  the  short  arm. 

Secondly.  Fill  with  mercury  to  within  20 
cm.  of  the  end  a  stout  glass  tube  80  cm.  long, 
closed  at  one  end.  Under  what  pressure  is 
the  20  cm.  of  air  in  the  tube?  Close  the  end 
of  the  tube  with  the  finger,  and  invert  it  in  a 
vessel  of  mercury.  Accurately  measure  the 
length  of  the  air-column,  and  also  the  height 
of  the  mercury-column,  above  the  level  of 
the  mercury  in  the  vessel.  What  supports  the 
mercury  in  the  tube?  Observe  what  the 
barometer-reading  is.  Why  is  the  mercury- 
column  less  in  height  than  that  in  the  barom- 
eter? Under  what  pressure  must  the  air  in 
the  top  of  the  tube  be  ?  How  does  the  ratio 
of  the  initial  and  present  volume  of  the  air  in 
the  tube  compare  with  that  of  the  pressures  it 
is  under  in  the  two  cases?  Make  several 
experiments  with  different  initial  volumes  of 
air,  and  ascertain  if  the  same  relation  holds 
good.  Express  as  a  law  the  relation  discovered. 

In  order  to  subject  the  same  volume  of  air  to  different 
pressures  less  than  one  atmosphere,  a  deep  cistern  of  mercury 
will  be  required.  To  provide  this,  close  one  end  of  a  heavy 
glass  boiler-tube  about  75  cm.  long  and  2.5  cm.  diameter,  and 


FIG.  78. 


110 


PRACTICAL  PHYSICS. 


insert  it  in  a  heavy  wooden  block  for  a  base.  Then,  instead  of 
closing  one  end  of  the  barometer-tube  used  by  fusion,  it  would 
be  better  to  cement  on  the  end  a  metal  ferrule,  into  which  is 
fitted  a  screw  for  closing  the  end.  With  such  an  arrangement, 
it  will  be  easy  to  regulate  the  amount  of  air  enclosed. 


III.    LAW    OF    PASCAL. 

166.  Apparatus.  —  Brass  Tube,  Haldat's  Apparatus,  Equi- 
librium Vases,  Glass  Tubing,  etc. 

167.  Exercise.  —  Procure  a  piece  of  brass  tubing  25  mm. 
in  diameter  and  25  cm.  long.      Fit  to  it  a  piston  made  by 

winding  candle-wick  around  one  end  of  a  piece 
of  barometer-tube  20  cm.  long  (Fig.  79).  Close 
one  end  with  a  perforated  cork.  Drill  holes 
through  the  side  of  the  tube  at  different  dis- 
tances from  the  open  end,  and  insert  perforated 
corks.  Fit  neatly  in  all  these  corks  glass  tubes 
of  such  a  length,  and  so  bent,  that  their  free 
ends  are  all  on  the  same  level,  and  at  least  5 
cm.  above  the  open  end  of  the  brass  tube.  Re- 
move the  piston,  fill  the  apparatus  nearly  full  of 
water,  and  then  insert  the  piston,  holding  the 
tube  in  a  vertical  position.  Compare  the  heights 
of  the  water  in  all  the  tubes  as  pressure  is 
applied  to  the  piston.  Why  does  the  water  rise 
in  each  tube?  How  does  the  direction  of  the 
applied  pressure  compare  with  that  of  the  motion  observed  in 
the  different  tubes  ?  What  is  to  be  learned  from  the  comparison 
of  the  heights  of  the  water  in  the  tubes  ?  Express  as  a  prop- 
osition the  truth  developed  by  this  experiment. 


FIG.  79. 


MECHANICS   OF  FLUIDS. 


Ill 


168.  Exercise.  —  Bend  a  stout  glass  tube  twice  at  right 
angles,  making  the  arms  25  cm.  and  12  cm.  long  respectively, 
and  the  distance  between  them  50  cm.     Set  this  in  a  frame  so 
that  these  arms  are  vertical  and  well  supported.     Take  a  glass 
tube   25   mm.  diameter  and   25   cm.  long,   a  lamp-chimney  of 
about  the  same  length,  and  a  two-litre  bottle  with  the  bottom 
removed  (see  p.  354)  ;   fit  to  each  of   these  a  cork  with  two 
holes,  through  which  pass  two  pieces  of  tubing  of  the  same 
bore,  so  arranged  that  one  of 

them  can  be  attached  to  the 
short  arm  of  the  U-shaped 
tube,  and  the  other  can  be 
closed  with  a  small  cork,  and 
be  used  as  an  emptying-pipe 
(Fig.  80).  Pour  mercury  in 
the  U-shaped  tube  till  it  rises 
8  or  10  cm.  in  the  long  arm. 
Now  attach  one  of  these 
vessels  by  a  short  rubber  con- 
nector to  the  U-shaped  tube, 

and  pour  in  water  till  nearly  full.  Mark  the  height  of  the 
water,  and  also  of  the  mercury,  in  the  long  arm.  Then  replace 
this  vessel  by  one  of  the  others,  and  fill  it  with  water  to  the 
same  height  as  in  the  first  case.  In  like  manner,  use  the  third 
vessel.  What  causes  the  mercury  to  rise  in  the  long  arm  each 
time  ?  Is  there  any  evidence  to  show  that  it  is  connected  with 
the  quantity  of  water  in  the  vessel  attached  to  the  short  arm  ? 
Any  evidence  that  it  is  connected  with  the  height?  What  truth 
is  taught  by  the  experiment? 

169.  Exercise.  —  Cut  out  of  wood   a  rectangular  block 
25  cm.  long,  10  cm.  wide,  and  5  cm.  thick.     Bore  a  hole  length- 


FIG.  80. 


112  PRACTICAL   PHYSICS. 

wise  through  the  stick  2  cm.  in  diameter.  Likewise  bore 
several  holes,  5  cm.  apart,  through  the  side  of  the  piece,  so  as 
to  connect  with  the  first  one.  Close  the  holes  with  perforated 
stoppers,  rubber  ones  if  you  have  them,  through  which  pass 
glass  tubes  bent  into  various  forms,  but  all  terminating  in  a 
line  parallel  to  the  stick  (Fig.  81).  Pour  water  through  one 


FIG.  81. 

of  them  till  it  rises  several  centimetres  in  that  tube.  Compare 
the  level  of  the  water  in  the  various  tubes.  What  causes  the 
water  to  rise  in  the  other  tubes  ?  Account  for  the  height 
attained  in  each  tube.  What  truth  is  taught? 

170.  Exercise.  —  Bore  a  hole  in  the  side  of  a  wooden  pail 
near  the  bottom,  and  insert  a  stop-cock.  A  perforated  cork, 
through  which  passes  a  glass  tube,  may  be  used  as  a  substitute, 
by  slipping  over  the  end  a  short  piece  of  rubber  tubing  closed 
with  a  pinch-cock.  Fill  the  pail  with  water,  place  it  on  a  chair 
on  the  table,  and  attach  a  piece  of  rubber  tubing  2  or  3  metres 
long  to  this  stop-cock.  In  the  other  end  of  this  tube,  insert  a 
jet-tube  secured  in  a  vertical  position  by  means  of  a  support 
standing  on  the  floor.  Open  the  stop-cock,  and  observe  closely 
the  attending  phenomenon.  Explain. 

Substitute  for  the  jet-tube  a  glass  tube  of  sufficient  length  to 
reach  to  the  level  of  the  water  in  the  pail.  Note  the  height 


MECHANICS   OF  FLUIDS.  118 

to  which  the  water  rises.  Account  for  the  difference  between 
the  height  reached  b}T  the  water  in  the  tube,  and  that  when 
escaping  as  a  jet.  Ascertain  what  the  height  of  the  jet 
depends  on,  by  comparing  the  conditions  under  which  different 
heights  are  obtained. 

f 
IV.    THE    SIPHON    AND    PUMP. 

171.  Apparatus.  —  Glass    and    Rubber    Tubing,    several 
large   Bottles,  small   Suction-Pump,   Air-Pump,  etc. 

172.  Exercise.  —  Bend  into  a  U -shape  a  glass  tube  about 
50  cm.  long.     Fill  the  tube  with  water,  close  one  end  with  the 
finger,  and  invert  it.      Why  does  not  the  water  run  out  of 
the  tube  ?     Now  let  each  end  dip  into  a  cylindrical  jar  partly 
filled  with  water.     Place  one  of  the  jars  on  a  block  of  wood, 
and  observe  the  motion  of  the  liquid.     Is  the  velocity  of  flow 
constant?     When  greatest?     When  least? 

Make  a  second  siphon  by  connecting  together  two  L-shaped 
glass  tubes  with  a  rubber  connector.  Ascertain  if  the  apparatus 
will  work  when  a  small  hole  is  made  in  the  side  of  the  rubber 
tube  between  the  two  glass  tubes.  Explain. 

Make  a  third  siphon  similar  to  the  first,  using  tubing  of 
about  1.5  mm.  bore  to  diminish  the  rate  of  flow.  Connect  two 
flasks  with  it,  place  the  apparatus  beneath  the  bell-jar  of  an 
air-pump,  and  then  quickly  exhaust  the  air. 

Examine  these  different  experiments,  and  frame  an  explana- 
tion of  the  action  of  a  siphon. 

173.  Exercise.  —  Make  a  siphon  out  of   a  rubber  tube. 
Let  the  outer  arm  be  a  few  centimetres  longer  than  the  inner 
one,   and  measure  the  amoant   of   flow  during   five   minutes. 


114  PRACTICAL   PHYSICS. 

Increase  the  length  of  the  outer  arm,  leaving  the  inner  arm 
unchanged,  and  again  measure  the  flow  during  five  minutes. 
Again  increase  the  length,  and  measure  the  flow.  On  what 
does  the  velocity  of  flow  depend  ? 

174.  Exercise.  —  Determine  the  law  which  regulates  the 
height  over  which  a  liquid  can  be  carried  by  a  siphon. 

Use  a  long  rubber  tube  of  small  bore  for  a  siphon,  and 
mercury  for  the  fluid.  Fill  the  tube  with  mercury,  and  tie  up 
the  ends  securely  with  wire.  After  placing  the  tube  in 
position,  with  its  ends  opening  in  dishes  having  different  levels, 
the  higher  containing  mercury,  open  the  ends,  and  gradually 
raise  the  bend  of  the  tube  till  a  position  is  reached  in  which  the 
flow  ceases,  but  is  resumed  on  lowering  it  in  the  least.  Compare 
the  height  of  this  above  the  surface  of  the  mercury  in  the  higher 
vessel,  with  the  barometer  reading  at  the  time. 

A  glass  siphon  of  small  bore  could  be  substituted  for  the 
rubber,  and  the  experiment  made  under  the  bell-jar  of  an 
air-pump,  the  reading  of  the  pump-gauge  being  taken  at  the 
instant  the  mercury-column  breaks  in  the  siphon,  and  this 
compared  with  the  height  of  this  column. 

175.  Exercise.  —  Devise   a    fountain    by   conducting   the 
water  from  a  vessel  to  a  jet-tube  by  means  of  a  siphon.     On 
what  does  the  height  of  the  jet  depend?     Why? 

176.  Exercise.  —  Construct  an  intermittent  fountain. 

Cut  off  the  bottom  of  a  large  bottle.  See  p.  354.  Cork  the 
mouth  of  the  bottle  with  a  perforated  cork  through  which 
passes  a  glass  tube,  reaching  to  within  2  or  3  cm.  of  the  end  of 
the  bottle.  Support  the  bottle,  mouth  downward,  in  the  ring 
of  the  iron  stand ;  place  a  long  test-tube  over  the  glass  tube, 


MECHANICS   OF  FLUIDS. 


115 


such,  that,  when  the  bottle  is  full  of  water,  the  upper  surface 
is  above  the  test-tube.  Arrange  a  siphon  with  an  adjustable 
pinch-cock  to  convey  water  from  some  large  vessel  to  the  bottle 
at  a  rate  somewhat  less  than  the  outlet-tube  can  empty  it.  Set 
the  siphon  in  operation,  and  notice  the  character  of  the  flow 
from  the  bottle.  Explain. 


177.  Exercise.  —  Select  three  bottles  of  about  one  litre 
capacity  each,  and  fit  to  them  corks  with 
two  holes.  Only  the  best  corks  can  be 
used.  Place  two  of  the  bottles  on  the 
table,  and  the  third  one  on 
the  floor.  Using  rubber  and 
glass  tubing,  connect  them 
as  shown  in  Fig.  82.  Now 
fill  the  bottles  on  the  table 
with  water,  leaving  the  one 
on  the  floor  filled  with  air, 
and  set  the  apparatus  in  op- 
eration by  blowing  through 
the  short  tube  of  the  farther 
bottle.  Explain.  Why  must 
the  corks  be  tight?  Find, 
by  varying  the  connections, 
upon  what  the  height  of  the 
jet  depends. 


FIG.  82. 


FIG.  83. 


178.    Exercise.  —  Fit  a  good   cork  to  an 
open-top   receiver.      Through   this   cork,   pass, 
air-tight,  a  glass  tube  reaching  to  the  bottom  of 
a  tumbler  of  water  within  the  receiver.      Connect  with  this 
tube  a  small  suction-pump  (Fig.  83).     Ascertain  whether  water 


116  PRACTICAL   PHYSICS. 

can  be  pumped  out  of  the  tumbler.  Then  place  the  apparatus 
on  the  table  of  an  air-pump,  exhaust  the  air,  and  ascertain  the 
effect  on  the  working  of  the  pump.  Inference. 


V.    THE    PRINCIPLE    OF  ARCHIMEDES. 

179.  Apparatus.  —  Balance,  Bucket  and  Cylinder  Appara- 
tus, Cylindrical  Graduate,  Cylindrical  Jar,  Air-Pump,  etc. 

180  Exercise.  —  Ascertain  the  effect  on  the  weight  of  a 
substance  produced  by  an  enveloping  fluid. 

Attach  a  heavy  weight,  stone  or  metal,  to  an  accurate  spring- 
balance,  and  take  the  reading.  Lower  the  weight  into  a  vessel 
of  water,  and  again  take  the  reading.  Inference. 

Repeat  the  experiment,  using  a  block  of  wood.  Inference. 
Under  what  condition  does  a  substance  appear  to  lose  all  of  its 
weight? 

Now  place  the  vessel  of  water  on  the  platform  of  a  balance, 
and  find  its  weight.  Suspend  each  of  the  above  articles  ID 
succession  from  the  hook  of  the  spring- balance,  submerging  it 
in  the  water  if  possible,  and  compare  the  difference  in  the 
weight  of  each  substance  caused  by  being  placed  in  water,  with 
the  change  produced  in  the  weight  of  the  vessel  of  water  as 
shown  by  the  balance.  Account  for  the  apparent  loss  of  weight 
in  the  first  two  experiments. 

Repeat  all  these  experiments,  substituting  strong  brine  for 
the  water.  Compare  the  weight  apparently  lost  with  that  appar- 
ently lost  when  water  was  used.  Compare  the  weight  apparently 
lost  by  a  large  piece  of  metal  with  that  apparently  lost  by  a 
small  piece  of  the  same  substance.  Compare  the  loss  appar- 
ently suffered  by  a  block  of  lead  with  that  apparently  suffered 


MECHANICS   OF  FLUIDS. 


117 


by  a  block  of  any  other  metal  of  the  same  size, 
the  amount  of  apparent  loss  depend  ? 


On  what  does 


181.  Exercise.  —  Find  the  measure  of  the  buoyant  force. 
Dealers  in  physical  apparatus  furnish  a  piece  known  as  the 

Bucket  and  Cylinder.  It  consists  of  a  cylindrical  brass 
bucket,  to  which  is  accurately  fitted  a 
brass  plug  (Fig.  84).  Hang  the  bucket 
from  one  arm  of  a  balance,  with  the 
plug  attached  below  it  by  means  of  a 
hook  and  thread.  Counterpoise  the 
two  cylinders  by  weights  in  the  other 
scale-pan.  Now  place  a  vessel  of 
water  beneath  the  apparatus,  so  that 
the  solid  cylinder  will  be  submerged 
when  the  beam  is  horizontal.  Why 
is  the  equilibrium  destroyed?  Pour 
water  into  the  bucket  till  the  equilib- 
rium is  restored.  How  much  water  is 
displaced  by  the  plug?  Compare  this 
amount  with  that  found  necessary  to  FlG- 84- 

restore  equilibrium.      How  much  weight   do  you  find  that  a 
submerged  body  apparently  loses  ? 

182.  Exercise.  —  A  second  method  of  finding  the  measure 
of  the  buoyant  force. 

Tie  a  fine  thread  or  hair  to  a  piece  of  metal  or  stone,  and 
suspend  it  from  one  end  of  a  balance-beam.  Many  balances 
have  a  hook  provided  for  attaching  any  substance  in  this  way. 
Weigh  the  substance ;  then  bring  a  vessel  of  water  beneath  it, 
arid  find  its  weight  when  submerged.  The  vessel  of  water  can 
be  supported  on  a  small  wooden  stool  placed  over  the  scale-pan 


118  PRACTICAL  PHYSICS. 

so  as  not  to  interfere  with  the  movement  of  the  balance. 
Determine  how  much  water  the  substance  will  displace  by 
proceeding  as  in  Art.  20.  Allowing  each  cubic  centimetre  of 
water  to  weigh  a  gramme,  how  does  the  weight  apparently  lost 
compare  with  the  weight  of  the  water  displaced?  State  as  a 
proposition  the  truth  proved. 

183.  Exercise.  —  Determine  the  principle  of  flotation. 
Weigh  a  piece  of  paraffine  or  varnished  wood,  then,  employing 

a  graduated  cylinder  containing  water,  determine  the  amount 
of  water  displaced  by  it  when  floating.  If  each  cubic  centi- 
metre of  water  displaced  weighs  one  gramme,  how  does  the 
total  weight  of  water  displaced  by  a  floating  body  compare  with 
the  weight  of  that  body  in  air?  Infer  from  this  when  a  body 
will  float  in  a  fluid.  Can  the  form  of  a  body  affect  the 
displacing  power  ?  Make  a  piece  of  lead  float  on  water  without 
attaching  any  thing  to  it. 

184.  Exercise.  —  Weight  a  small  test-tube,  so 
that,  when   placed   in  a  vessel   of   water,   mouth 
downward,    it   will    float,    maintaining   a   vertical 
position    (Fig.  85).      Fill   a   cylindrical   jar   with 
water  to  within  a  few  centimetres  of  the  top,  place 
in  it  the  test-tube,  and  set  the  apparatus  beneath  a 
bell-jar  on  the  table  of  the  air-pump.     Gradually 
exhaust  the  air,  letting  it  re-enter  the  bell-jar  quite 
frequently,  to  determine  whether  that  point  has  yet 
been  reached  at  which  the  test-tube  is  nearly  on  the 
point  of  sinking  owing  to  air  having  been  removed: 
from   it.      When   that   point  is  reached,   remove 

rIG.  so. 

the  jar  from  the  air-pump,  and  tie  over  the  top 

a  piece   of   sheet-rubber.      Now,   by  pressing  on  the  top  of 


MECHANICS   OF  FLUIDS. 


119 


the  rubber,  the  tube  can  be  made  to  sink  to  any  desired  point 
within  the  jar.  Observe  the  level  of  the  water  in  the  tube  as 
it  is  made  to  occupy  different  positions  by  varying  the  pressure. 
Explain  the  action  of  the  apparatus,  pointing  out  all  the  prin- 
ciples illustrated  by  it. 

In  case  a  sufficiently  tall  bell-jar  is  not  at  hand,  the  necessary 
amount  of  air  can  be  removed  by  means  of  a  J-shaped  tube, 
the  short  arm  of  which  is  about  as  long  as  the  test-tube.  By 
holding  the  test-tube  over  the  short  arm  of  the  J-tube  as 
you  let  it  down  into  the  water,  the  air  will  escape  through 
this  tube,  water  taking  its  place.  After  a  few  trials,  it  will 
be  found  easy  to  remove  the  proper  amount. 

185.  Exercise.  —  Ascertain  if 
air  affects  the  apparent  weight  of 
substances. 

Place  beneath  a  large  bell-jar 
on  the  table  of  an  air-pump  a 
short  -  beam  jeweller's  balance, 
having,  in  place  of  the  scale-pans, 
a  large  cork  or  glass  float  and  a 
piece  of  lead  accurately  balanced 
(Fig.  86).  Exhaust  the  air,  and 
note  the  effect  on  the  balance. 
Repeat  several  times  to  make  it 
certain  that  the  phenomenon  at- 
tending the  exhaustion  is  not 

accidental.  Explain.  How  can  the  weight  of  an  object 
obtained  in  air  be  reduced  to  that  in  a  vacuum? 


FIG.  86. 


120 


PRACTICAL   PHYSICS. 


VI.    DETERMINATION    OF    DENSITY. 

186.  Apparatus.  —  Balance,  Cylindrical    Graduate,  Spe- 
cific-gravity Bottle,  Hydrometers,   Florence   Flask,  Air-Fump, 
Glass  Tubing,  etc. 

187.  Exercise.  —  Determine,  by  means  of  a  balance,  tha 
density  of  a  solid  insoluble  in  water. 

Suspend  the  substance,  by  means  of  a  fine  thread  or  hair, 
from  the  hook  on  the  bail  of  the  scale-pan  provided  for  that 
purpose,  and  determine  carefully  its  weight.  As  in  Art.  182, 
find  its  weight  in  water.  From  these  data  determine  the  volume 
of  water  displaced  by  the  solid.  Divide  the  weight  in  the  air 
by  the  volume,  and  the  density  is  obtained.  This  result  needs 
correcting  for  temperature,  pressure,  etc.,  when  great  accuracy 
is  required. 

As  a  check,  divide  the  weight  in  air  expressed  in  grammes 
by  the  volume  in  cubic  centimetres,  as  determined  by  the 
method  of  Art.  20. 

Tabulate  results  as  follows  :  — 


Name  of 
Substance. 

Weight 
in  Air. 

Volume, 
ccm. 

Density. 

Weight 
in  Water. 

Density. 

Average. 

Glass    .     .     . 

Iron     .     .     . 

Lead    .     .     . 

Marble      .     . 

Copper     .     . 

etc. 

MECHANICS   OF 'FLUIDS.  121 

188.  Exercise.  —  Determine  the   density  of   a   substance 
lighter  than  water. 

As  in  the  last  experiment,  determine  the  weight  in  air,  and 
also  the  weight  of  a  piece  of  lead  or  other  metal  of  sufficient 
mass  to  sink  the  specimen  in  water.  Then  determine  the 
weight  of  the  sinker  in  water,  and  also  of  the  specimen  and 
sinker  combined.  From  these  data,  the  volume  of  the  water 
displaced  by  the  substance  is  easily  obtained.  How?  Divide 
the  weight  in  air  by  the  volume,  and  the  required  density  is 
obtained. 

Check  this  in  the  same  manner  as  in  the  last  experiment. 

189.  Exercise.  —  Determine  the  density  of   a   substance 
soluble  in  water. 

As  in  Art.  182,  find  the  weight  of  an  equal  volume  of  some 
liquid  of  known  density  in  which  it  is  insoluble.  This  divided 
by  the  density  of  that  liquid  will  give  the  volume  of  the 
substance.  Why?  Now  proceed  as  in  Art.  187. 

Rock-salt  is  insoluble  in  naphtha,  rock-candy  and  saltpetre  in 
strong  alcohol,  alum  and  blue  vitriol  in  oil  of  turpentine,  etc. 

190.  Exercise.  —  Determine  the  density  of  a  liquid. 

For  accurate  work,  use  the  specific-gravity  bottle.  It  is  a 
small  flask  holding  usually  10,  25,  50,  or  100  ccm.,  closed  with 
an  accurately  fitting  glass  stopper,  through  which  is  a  small 
capillary  opening.  Thoroughly  clean  the  bottle,  rinsing  it  out 
finally  with  strong  alcohol,  and  dry  by  forcing  into  it  a  stream 
of  air  passing  through  a  heated  tube.  After  weighing  the 
bottle,  ascertain  its  capacity  if  not  already  known,  then  fill  it 
with  the  liquid  whose  density  is  sought,  wiping  the  exterior  of 
the  bottle  dry,  and  removing  the  excess  of  the  liquid  that 
escapes  through  the  hole  in  the  stopper,  and  find  its  weight. 


122  PRACTICAL  PHYSICS. 

Deducting  the  weight  of  the  empty  bottle,  divide  the  remainder 
by  the  volume  of  the  bottle,  and  you  have  the  density.  This 
result,  when  great  accuracy  is  required,  must  be  corrected  for 
temperature,  etc.  Consult  Stewart  and  Gee's  "  Practical 
Physics,"  vol.  i. 

For  approximate  work,  a  small  Florence  flask  may  be  used, 
filling  it  with  water  up  to  a  line  marked  on  the  neck. 

191.  Exercise.  —  Determine   the  density  of   a  liquid   by 
weighing  a  solid  in  it. 

Make  a  sinker  out  of  a  thick  piece  of  glass  rod.  Fasten  it 
by  a  fine  thread  to  the  hook  on  the  frame  of  the  scale-pan. 
Find  the  apparent  loss  of  weight  of  the  sinker  in  water,  and 
in  the  liquid  whose  density  is  sought.  What  does  this 
apparent  loss  represent?  Divide  the  apparent  loss  in  the 
liquid  by  the  apparent  loss  in  water,  and  the  quotient  will  be 
the  density. 

192.  Exercise.  —  Determine  the  density  of  a  substance  in 
a  state  of  powder. 

Use  the  flask  of  Art.  190,  find  its  weight,  then  re-weigh  it 
after  filling  it  part  full  of  the  powder.  Now  cover  it  with  water, 
place  it  beneath  the  bell- jar  of  the  air-pump,  and  exhaust  the 
air,  the  water  taking  the  place  of  the  air  within  the  powder. 
If  the  substance  is  soluble  in  water,  some  other  liquid  must  be 
used.  On  removing  the  flask  from  the  pump,  ascertain  the 
weight  after  filling  it  full  of  water.  Let  /  =  weight  of 
the  flask,  w  =  weight  of  substance  after  deducting  weight 
of  the  flask,  wr  =  weight  of  substance  when  covered  with 
water,  w"  =  weight  of  water  required  to  fill  the  flask  when  the 
substance  is  removed.  Then  w'  —  w  =  weight  of  water 
added  to  fill  the  flask  when  the  substance  was  in  it,  and 


MECHANICS   OF  FLUIDS. 


123 


w"  _  (w'  _  w)  =  weight  of  water  whose  volume  is  that  of  the 
substance.     Therefore  the  density  = 


w"  —  w' 


193.    Exercise.  —  Determine  the  density  of  a  solid  with 
Nicholson's  hydrometer. 

This  instrument  usually  consists  of  a  metal  cylinder  with 
conical  ends,  to  the  vertices  of  which  are  soldered  stout  wires. 
On  the  end  of  one  wire  is  soldered  a  small 
scale-pan,  and  on  the  other  a  perforated 
pan  (Fig.  87).  The  lower  end  of  the 
cylinder  is  loaded  with  shot  so  that,  when 
the  apparatus  is  placed  in  water,  it  takes 
a  vertical  position  with  the  cylindrical  part 
nearly  submerged. 

To  use  this  apparatus,  place  on  the 
upper  pan  a  sufficient  number  of  known 
weights  to  sink  it  to  a  mark  on  the  stem 
just  below  the  scale-pan.  Let  a  represent 
the  number  of  grammes  required.  Then 
place  on  the  pan  the  substance  whose  density  is  required,  and 
add  weights  till  the  instrument  sinks  to  the  mark  on  the 
stem.  Let  b  represent  the  number  of  grammes  added.  Then 
a  —  b  =  the  weight  of  the  substance.  Now  transfer  the 
substance  to  the  lower  pan,  tying  it  on  if  necessary,  and 
observe  how  many  weights  must  be  added  to  the  b  weights  to 
sink  the  instrument  to  the  mark  on  the  stem.  Let  c  represent 


the  number  of  grammes  necessary.      Then 
Why? 


a  -  b 


—  density. 


194.    Exercise.  —  Determine  the  density  of   a   substance 
with  the  Jolly  balance. 


124 


PR  A  C  TIC  A  L   PH  YSICS. 


Solids  are  weighed  as  directed  in  Art.  24,  but  with  the  lower 
pan  attached,  and  immersed  in  water.  The  weight  in  water  is 
obtained  by  placing  the  substance  on  the  lower  pan. 

To  find  the  density  of  a  liquid,  weigh  a  solid  insoluble  in  it, 
first  on  the  upper  pan,  then  on  the  lower  pan  when  immersed 
in  water,  and  finally  on  the  lower  pan  when  immersed  in  the 
liquid.  Then  proceed  as  in  Art.  191. 

195.  Exercise.  —  Determine  the  density  of  a  liquid  by 
means  of  a  Nicholson's  hydrometer. 

Weigh  the  instrument,  then  place  it  in  water,  adding  weights 
to  the  upper  pan  till  it  sinks  to  the  mark  on  the  stem.  The 
weight  of  the  water  displaced  by  the  instrument  will  be  the  sum 
of  the  weights  on  the  pan  and  that  of  the  instrument.  Why? 
In  like  manner,  determine  the  weight  of  the  liquid 
displaced,  whose  density  is  required.  From  these 
data,  the  density  is  easily  determined.  How? 

For  corrosive  liquids,  a  glass  hydrometer  must 
be  used.  In  such  instruments,  the  lower  pan  is 
usually  omitted. 


196.  Exercise.  —  Make  out  of  light  wood  a 
bar  of  uniform  size  throughout,  having  a  length 
of  30  cm.  and  a  cross-section  of  1  scm.  Bore  a 
hole  several  centimetres  deep  into  one  end,  and 
put  in  pieces  of  lead  sufficient  to  maintain  the  bar 
in  a  vertical  position  when  floating  in  water,  closing 
the  hole  with  cement.  Lay  off  on  the  bar  a  decimal 
scale,  the  zero  at  the  loaded  end.  Give  the  apparatus  a  thin 
coat  of  paraffine.  Now  float  the  instrument  in  a  vessel  of 
water,  and  note  the  division  of  the  scale  to  which  it  sinks ; 
then  place  it  in  the  liquid  whose  density  is  sought,  and  take  the 


FIG.  88. 


MECHANICS   OF  FLUIDS. 


125 


reading.    The  quotient  of  the  former  by  the  latter  is  the  density 
of  the  liquid.     Why? 

For  accurate  determinations,  especially  of  corrosive  liquids, 
glass  hydrometers  (Fig.  88)  with  graduated  stems  are  usually 
employed.  The  method  of  use  is  similar  to  that  illustrated 
above. 

Make  a  five-per-cent,  a  ten-per-cent,  and  a  twenty-per-ceut 
solution  of  common  salt,  and  determine,  by 
means  of  the  hydrometer  of  constant  weight, 
the  density  of  each.      Verify  the  results  by 
some  one  of  the  methods  already  given. 

197.  Exercise.  —  Fit  a  rubber  stopper  with 
two  holes  to  a  small  Florence  flask.     In  this 
stopper,  insert,  air-tight,  two  glass  tubes,  each 
75  cm.  long,  and  bent  twice  at  right  angles  at 
the  end  next  the  cork  (Fig.  89),  so  that  the 
tubes  will  not  stand  so  close  together.     Sup- 
port   the    apparatus    in    a   vertical    position, 
with   the   end    of    one    tube    dipping   into   a 
beaker  of  water,  and  the  other  into  a  vessel 
containing  the  liquid  whose  density  is  sought. 
Carefully  measure  the  capillary  effect.     Now 
gently  warm  the  flask  till  part  of  the  air  is  ex- 
pelled.    When  cold,  the  liquids  having  ceased 

to   rise,  measure   the   height   of   each   liquid  Fie<  89- 

above  that  in  the  vessel.     The  ratio  of  these  heights  corrected 
for  capillarity  will  be  the  inverse  ratio  of  their  densities. 

198.  Exercise.  —  Determine  the  density  of  air. 

Fit  to  a  stout  Florence  flask  of  about  one  litre  capacity  a 
rubber  stopper  through  which  is  inserted  a  good  stop-cock. 


126  PRACTICAL  PHYSICS. 

Dry  the  flask,  and  determine  its  weight.  Then  exhaust  the  air 
as  completely  as  possible,  reading  the  pressure-gauge  on  the 
pump  as  well  as  the  barometer.  Weigh  the  exhausted  flask, 
then  measure  its  capacity,  and  compute  from  these  data  the 
weight  of  one  cubic  centimetre  of  air,  that  is,  its  density. 
The  capacity  of  the  flask  can  be  found  by  weighing  it  full 
of  water. 

For  more  accurate  methods,  consult  Roscoe  and  Schorlem- 
mer's  "  Chemistiy,"  vol.  iii.  pt.  i. 


HEAT.  127 


CHAPTER    IV. 

HEAT, 
I.    HEAT,    AND    MECHANICAL    MOTION. 

199.  Apparatus.  —  Flint  and  Steel,  Fire-Syringe,  Tinder, 
Bottles,  Thermometer,  Metal  Rod,  Tumblers,  Mercury,  Whirl- 
ing-Machine,   Air-Thermometer,    Condensing-Pump,   Air-Pump, 
Florence   Flasks,   Pyrometer,   Radiometer,  etc. 

200.  Exercise.  —  Hold  a  piece  of  hardened  steel,  as  the 
back  of  the  blade  of  a  large  pocket-knife,  between  the  thumb 
and  forefinger  of  the  right  hand,  and  strike  a  glancing  blow 
against  the  sharp  edge  of  a  piece  of  flint.     Observe  any 
attending   phenomena.      Examine   the   substances   after 
striking  them  together  a  few  times.      Is  there  any  evi- 
dence of  any  quantitative  connection  between  the  energy 
expended  and  the  heat  obtained  ? 

201.  Exercise.  —  Place   a   small  piece   of    German 
tinder  in  the  cavity  at  the  end  of  the  piston  of  a  Fire- 
Syringe  (Fig.  90)  ,  and  force  it  quickly  into  the  cylinder. 
Remove  the  piston   as   soon   as   possible,  and  examine 
the    tinder.      After    each    introduction    of    the    piston, 
fresh   air  must  be   introduced   into  the  tube  to  supply 


If  the  syringe  has  a  glass  cylinder,  introduce  within 
it  a  pellet  of  cotton-wool  moistened  with  carbon  disulphide. 


128  PRACTICAL  PHYSICS. 

Remove  it  after  it  has  remained  a  few  moments,  and  force  in 
the  piston,  keeping  a  close  watch  on  the  tube. 

Account  for  the  phenomenon  attending  this  experiment. 

202.  Exercise.  —  Fill  a  bottle  of  about  four  ounces  capacity 
half  full  of  water,  and  take  the  temperature  with  a  thermometer. 
The  water  should  be  at  the  temperature  of  the  room.      Now 
cork  the  bottle,  wrap  it  up  in  several  thicknesses  of  paper  to 
keep  heat  from  being  communicated  to  it  from  the  hand,  shake 
vigorously  for  an  observed  number  of  minutes,  and  again  take 
the  temperature.     Ascertain  the  effect  of  increasing  the  time 
of  shaking.     Is  there  any  evidence  of  any  connection  between 
the   amount  of  motion   and  the  heat?      Devise   some  way  of 
showing   that   the    rise    in   temperature   was   not  due  to   heat 
communicated  to  the  water  from  the  hand. 

203.  Exercise.  —  Rub  a  metal  rod  vigorously  with  a  piece 
of   leather  for   a   few  minutes,   protecting   the    rod   from    the 
heat  of  the  hand  by   a   paper  holder.      Touch  the   rod  to  a 
piece  of  phosphorus.      Inference.      Have  you  any  equivalent 
for  the  energy  expended  in  rubbing  the  rod?     Is  there  any 
evidence  of  any  quantitative  relation  between  the  heat  devel- 
oped and  the  energy  expended?     If  energy  is  indestructible, 
what  would  you  infer  is  the  nature  of  heat  ? 

Caution.  —  Always  cut  phosphorus  under  water,  and  never  handle  it 
with  dry  fingers. 

204.  Exercise.  —  Wrap  each  of  two  tumblers  with  several 
thicknesses   of    paper   to   keep   from   them   the   heat    of    the 
hand.      Fill  one  of  the  tumblers   one-third  full  of  mercury, 
and   determine   its    temperature   by  inserting  a  thermometer. 
Then,  pour  the  mercury  rapidly,   in  a  stream  as  large  as  a 


HEAT. 


129 


slate-pencil,  back  and  forth  between  the  tumblers  for  five 
times,  letting  the  mercury  fall  from  a  height  of  about  25  cm. 
Take  the  temperature.  Ascertain  the  effect  of  ten  pourings  ; 
twenty.  Repeat  these  tests,  letting  the  mercury  fall  50  cm. 
Inference. 

The  mercury  should  be  at  the  temperature  of  the  room  at  the 
beginning  of  each  set  of  pourings. 

205.  Exercise.  —  Attach  to  a  whirling-machine  a  brass 
tube  about  15  cm.  long  and  15  mm.  diameter  (Fig.  91).  Fill 
it  half  full  of  alcohol,  and  close  the  end  with  a  cork.  Rotate 


c-w 


FIG.  91. 


the  apparatus  rapidly,  applying  a  brake  made  of  two  pieces 
of  board  hinged  at  one  end  with  a  strip  of  leather,  and  also 
Covered  with  leather  at  the  places  of  contact  with  the  tube.  In 
a  few  minutes,  the  alcohol  can  be  made  to  boil  vigorously,  as 
the  experimenter  will  find  ample  evidence.  Account  for  the 
heat. 


130 


PRACTICAL  PHYSICS. 


206.  Exercise.  —  Blow  a  stream  of  air  with  a  small  bellows 
against  the  bulb  of  a  sensitive  thermometer,  or  the  face  of  a 
thermopile  (Fig.  114),  and  record  the  effect.     Explain. 

207.  Exercise.  —  Compress  air  within  the  copper  reservoir  of 
the  condensing-pump,  obtaining  as  high  a  pressure  as  possible. 
After  the  apparatus  has  stood  long  enough  to  acquire  the  tem- 
perature of  the  room,  turn  the  stop-cock,  directing  the  escaping 
air  against  the  bulb  of  a  thermometer,  or  the  face  of  the  thermo- 
pile, and  record  the  effect.     Whence  does  the 

air,   on   escaping,   acquire   its  kinetic   energy? 
Devise  some  way  of  proving  your  answer. 

Suspend  a  thermometer  within  the  receiver 
of  the  air-pump,  observing  the  effect  as  the 
exhaustion  proceeds.  Explain. 

208.  Exercise.  —  Fit,  air-tight,  to  a  Flor- 
ence   flask    a    cork    through    which    passes    a 
J-shaped   tube   reaching  nearly  to  the  bottom 
of  the  flask,  and  a  thermometer  with  the  bulb 
at  the  centre  of  the  flask  (Fig.  92).     Fill  the 
flask  a  little  less  than  half   full   of  water  at 
the  temperature  of  the  room,  and  hold  it  sub- 
merged in  a  vessel  of   boiling    water   for   30 
seconds.    Note  carefully  the  effect  produced  on 
both  the  water  of  the  flask  and  the  thermometer. 
Now  remove  the  J-tube,   and  close,   air-tight, 
the  opening  in  the  cork.     Change  the  water  in 

the  flask  for  an  equal  amount  of  water  of  the  temperature  of  the 
room.  Again  hold  the  flask,  for  30  seconds,  in  a  vessel  of 
boiling  water,  and  record  the  reading  of  the  thermometer. 
Account  for  the  difference  of  temperature  in  the  two  cases. 


FIG.  92. 


HEAT. 


131 


It  will  be  necessary  to  hold  the  cork  in  the  flask,  or  the  elastic 
force  of  the  air  will  throw  it  out,  and  break  the  thermometer. 

209.  Exercise.  —  Fasten  a  metal  rod  about  30  cm.  long  to 

a  wooden  block  by  means 
of  small  wire  staples,  the 
block  to  be  attached  to  a 
board  for  a  base.  To  the 
opposite  end  of  the  board, 
tack  a  thin  piece,  to  sup- 
port an  index  against 
which  rests  the  free  end 
FIG-93-  of  the  rod  (Fig.  93).  The 

pointer  may  be  cut  out  of   tin  or  brass, 

and  should  have  the  pivot  distant  but  a 

couple  of  millimetres  from  the  end  of  the 

rod.      Place  a  spirit  or  gas  flame  under 

the  rod  for  a  few  minutes,  and  watch  the 

effect. 

Fasten  the  end  of  the  pointer,  by  an 

elastic,  to  a  pin,  and  see  if  the  expanding 

rod  does  work  by  stretching  the  elastic. 

Whence  the  energy  expended  in  doing  this 

worK  ? 

210.  Exercise.  —  Place  a  Radiometer 
(Fig.  94)  in  a  beam  of  sunlight,  or  in  the 
light  from  a  gas-jet  admitted  through  an 
opening  cut  in  a  large  sheet  of  cardboard, 
and  notice  the  effect  on  the  instrument. 
Try  a  Bunsen  or  spirit  flame  which  emits 

heat  and  but  little  light.      Interpose  between  the  radiometer 


FIG.  94. 


132  PRACTICAL   PHYSICS. 

and  the  source  of  light  a  chemical  tank  (Fig.  234)  or  flat  bottle 
filled  with  alum-water,  a  substance  which  cuts  off  but  little  light 
and  most  of  the  heat.  Substitute  a  solution  of  iodine  in  carbon 
disulphide  in  place  of  the  alum- water,  thus  cutting  off  the  light, 
and  but  little  of  the  heat.  Inference. 


II.    HEAT,   AND    CHEMICAL  ACTION. 

211.  Apparatus.  —  Test-Tube,  Thermometer,  Saucer,  Mor- 
tar, etc. 

212.  Exercise.  —  Fill  a  test-tube  one-third  full  of  water, 
and  take  its  temperature  with  a  thermometer.     Fill  a  second 
one   one-third    full   of   sulphuric   acid,   and   likewise  take   its 
temperature.      Now  pour  the  acid  in  a  fine  stream  into  the 
water,  and  record  the  temperature.     Inference. 

213.  Exercise.  —  Place  in   a  common  saucer  a  lump  of 
freshly  burned  quicklime  as  large  as  a  hen's  egg.     Ascertain 
its  temperature  by  placing  the  bulb   of   the  thermometer  in 
contact  with  it  for  a  few  minutes.     Now  fill  the  saucer  with 
water,  and,  after  a  few  minutes,  take  the  temperature  of  the 
lime.     Explain. 

214.  Exercise.  —  Powder  in  a  mortar   some   crystals   of 
cupric   nitrate.       Spread   the   powder   thickly   on    a   piece   of 
tin-foil    about    10    cm.  square.       Sprinkle   on   the   powder   a 
small  quantit}T  of  water,  and  quickly  wrap  it  up  in  the  foil, 
pressing  down  the  edges.      Notice  the  changes  which  follow. 
Explain. 


HEAT.  133 

III.    CONDUCTION    OF    HEAT. 

215.  Apparatus.  —  Thermometer,    Conductometer,    Rods 
of  different  kinds  of  material,  Cylinder  of  Brass,  and  one  of 
Wood,    Lead    Balls,    Brass    Wire-Cloth,    Wooden    Cube,    Air- 
Thermometer,  etc. 

216.  Exercise,  —  Take  the  temperature  of  several  different 
articles  in  a  room,  at  about  the  same  distance  from  the  floor, 
by  holding  the  bulb  of  the  thermometer  in  contact  with  each 
successively  for  a  few  minutes.     Now  test  the  same  substances 
as  to  temperature  by  touching  them  with  the  hand.     Which 
substances  feel   cold,   and  which  do  not?      Account   for  the 
differences   between   the   conclusions   based   on   the   sense   of 
touch,  and  those  on  the  indications  of  the  thermometer. 

217.  Exercise.  —  Compare    the    conductivity   of    several 
substances. 

Get  a  tin-smith  to  construct  a  tin  dish  with  small  tubes  on  the 
side,  in  which  can  be  cemented  rods  of  different  substances,  as 
iron,  copper,  zinc,  brass, 
etc.  (Fig.  95).  Coat 
these  rods  with  a  thin 
layer  of  beeswax ;  then  | 
fill  the  tank  with  hot 
water,  and  compare  the  1 
rates  at  which  the  wax 
melts  on  the  rods.  FIG  g. 

As  the  four  substances 

mentioned  differ  but  little  in  their  capacity  for  heat,  the  rates 
of  transference  of  temperature  will  not  differ  much  from  those 
for  transference  of  heat. 


134 


PRACTICAL   PHYSICS. 


218.  Exercise.  —  Wrap  firmly  around  a  brass  cylinder  a 
layer  of  writing-paper,  hold  it  in  the  flame  of  a  lamp,  and 
record  the  time  required  to  set  the  paper  on  fire.     Then  wrap  a 
similar  piece  around  a  wooden  cylinder  of  the  same  size,  and 
hold  it  in  the  flame  till  the  paper  burns.      Account  for  the 
difference  in  the  times. 

219.  Exercise.  —  Compare  the  thermal  conductivity  of  iron 
and  copper. 

Select  a  stout  wire  of  each,  35  cm.  long,  twist  them  together 
for  about  10  cm.,  and  then  insert  the  twisted  end  through  a 

wooden  frame,  the  untwisted 
parts  being  separated  (Fig. 
96).  Attach  lead  balls  or 
marbles  to  the  wires  at  reg- 
ular intervals  between  the 
supports,  using  shoemaker's 
wax  for  the  purpose.  Place  a 
spirit-lamp  under  the  twisted  part,  and  record  the  effect  on  the 
balls.  Inference. 

220.  Exercise.  —  Support  a 
piece  of  brass  wire-cloth  on  the 
ring  of  the  iron  stand,  place  a 
gas-flame  beneath  it,  and  record 
the  effect  on  the  flame  (Fig.  97). 
Test  for  gas  above  the  gauze  by 
applying  a  lighted  match.     Ac- 
count for  the  flame's  not  ex- 
tending through  the  gauze  at 
first.      Now  let  the  wire-cloth 

cool,   then   turn   on   the   gas,    and   light   it   above   the   cloth. 


FIG.  96. 


FIG.  97. 


HEAT.  135 

Account  for  its  burning  above  the  wire-cloth,  and  not  below. 
Observe  the  manner  in  which  gum-camphor  burns  when  placed 
on  the  wire-cloth. 

221.  Exercise.  —  Compare  the  conductivity  of  wood  with 
the  grain,  with  that  across  the  grain. 

Coat  uniformly  with  paraffine  three  of  the  faces  about  one 
corner  of  a  wooden  cube  5  cm.  on  the  edge.  Heat  a  metal  ball 
of  2.5  or  3  cm.  diameter  in  boiling  water,  and  place  it  as 
quickly  as  possible  on  one  of  the  waxed  faces  of  the  cube. 
Compare  the  shapes  of  the  melted  spots  formed  on  the  different 
sides,  and  account  for  the  difference.  The  ball  must  remain 
on  the  block  the  same  length  of  time  in  each  case.  Try  cubes 
made  from  pine,  oak,  maple,  etc. 

Wipe  the  water  off  of  the  ball  before  placing  it  on  the 
wax. 

222.  Exercise.  —  Test  the  conductivity  of  water. 

Place  in  a  long  test-tube  some  fragments  of  ice.  Fill  the 
tube  nearly  full  of  water,  keeping  the  ice  from  floating  by 
means  of  a  small  marble  or  stone.  Hold  the  tube  in  an 
inclined  position  in  a  Bunsen  or  spirit  flame,  heating  the  part 
near  the  surface.  Compare  the  temperature  of  the  water  at 
the  bottom  with  that  at  the  top  on  its  coming  to  a  boil. 
Inference. 

In  heating  the  tube,  pass  it  slowly  backward  and  forward 
through  the  flame,  as  a  sudden  application  of  heat  is  liable  to 
break  the  tube.  Why? 

223.  Exercise.  —  Cork  the  neck  of  a  large  funnel,  and 
through  it  pass  the  stem  of  an  air-thermometer,  bringing  the 
bulb  below  the  surface  of  the  funnel.     Support  the  apparatus 


136 


PRACTICAL   PHYSICS. 


as  shown  in  Fig.  98.  Fill  the  funnel  with  water  till  the  bulb 
of  the  air-thermometer  is  covered  to  the  depth  of  a 
centimetre.  Pour  a  spoonful  of  ether  on  the  water, 
set  it  on  fire,  and  record  the  effect  on  the  thermom- 
eter. Inference. 

The  lower  end  of  the  thermometer- tube  should 
dip  into  colored  water.  By  warming  the  bulb 
with  a  gas-flame  before  introducing  water  into 
the  funnel,  some  of  the  air  can  be  expelled 
from  the  bulb,  so  that,  on  cooling,  water  will 
FIG.  98.  stand  at  an  elevation  of  a  few  centimetres  in 

the  tube. 


IV.    CONVECTION    OF    HEAT. 

224.  Apparatus.  —  Florence  Flasks,  Glass  Tubing,  Lamp- 
Chimneys,  tall  Bell-Jar,  large  Bottle,  etc. 

225.  Exercise.  —  Fill  a  large  Florence  flask  two-thirds  full 
of    water,    introduce    a    little    powdered    cochineal    or    paper 
raspings,  and  apply  heat  by  placing  it  on  a  sand-bath  on  the 
iron  stand.     Make  a  careful  study  of   the  action  of  the  par- 
ticles,   to    ascertain    if    any   law   governs    their    movements. 
Explain. 

226.  Exercise.  —  Construct  out  of  glass  tubing  a  rectangle 
about   12   cm.  long  by  50  cm.  wide,   making  the   connections 
with  rubber  tubing.     A  T-tube  should  be  inserted  at  one  corner 
for  convenience  in  filling,  and  to  provide  for  the  expansion  of 
the  water.      Fill  the  apparatus  with  water  freed  from  air  by 
boiling,  and  introduce  a  little  powdered  cochineal.     Now  hold 
one  corner  of   the  apparatus  in  a  vessel  of  hot  water,  and 


HEAT. 


137 


observe  the  effect  on  the  water  in  the  tube.  Apply  ice  or  snow 
to  the  upper  corner  of  the  rectangle,  and  record  the  effect. 
Make  the  application  at  other  points.  Account  for  the  results. 

227.  Exercise.  —  Support  a  short  piece  of   candle  in  a 
vertical  position  in  the  bottom  of  a  common  plate.     Light  the 
candle,   and   place  over  it  a   wide  cylindrical   lamp-chimney. 
Pour  water  into  the  plate  to  prevent  air  entering  the  chimney 
at   the    bottom.      Note   the    effect    on    the   flame.      Insert   a 
cardboard    partition    in    the    chimney,   reaching  nearly  to  the 
Hame,   and  note  the  effect.      Soak  some   porous   paper  in  a 
solution  of  saltpetre,  and  dry  it  thoroughly.      This  is  known 
as  touch-paper,  and  burns  with  the  emission  of  considerable 
smoke.     Hold  a  piece  of  burning  touch-paper  over  the  top  of 
the  chimney,  and  make  a  study  of  the  air  circulation. 

228.  Exercise.  —  Paste  paper  over  the  cracks  of  a  common 
chalk-box  to  make  it  air-tight.      Near  one  end  of  the  cover, 
make   a  number  of  small   holes   in   a 

circle  somewhat  smaller  than  the  base 
of  a  lamp-chimney  (Fig.  99).  In  the 
centre  of  this  ring,  place  a  lighted 
taper.  Near  the  other  end  of  the 
cover,  cut  a  hole  25  mm.  in  diameter. 
Place  a  lamp-chimney  over  each  of 
these  openings,  coating  the  edge  of 
each  with  paraffine  to  produce  an  air- 
tight joint.  Study  the  air  currents 
through  the  apparatus  by  holding 
burning  touch-paper  over  the  tops  of 

the  chimneys.  Ascertain  the  effect  of  closing  the  top  of  the 
chimney  not  containing  the  taper. 


FIG.  99. 


138 


PRACTICAL   PHYSICS. 


229.  Exercise.  —  To  a  tall  wide-mouthed   jar,  fit  a  cork 
ring  supporting  a  wide  glass  chimney.     Place  the  jar  over  a 
candle  standing   in  a  plate  of  water.      After   observing   the 
effect  on  the  flame,  insert  in  the  chimney 

a  smaller  one  extending  down  nearly  to 
the  flame,  supporting  it  by  a  wire  frame 
(Fig.  100).  Study  the  air-currents  with 
touch-paper. 

Paper  cylinders  may  be  substituted   for 
the  chimneys. 

230.  Exercise.  —  Invert  a  tall  jar,  at 
least    50   cm.  high,   over  a  stand   support- 
ing several   tapers 

<^~^  (Fig.   101).       The 

stand  may  be  made 
by  inserting  a  stout 
wire  into  a  circular 
piece  of  board  for 

^ Oa  base,  supporting 

!p  the  tapers  on  wire  FIG.  100. 

arms  made  to  re- 
tain their  places  on  the  standard  by 
the  friction  of  the  spiral  formed  on 
one  end.  Observe  the  order  in  which 
the  tapers  are  extinguished.  Why  do 
the  tapers  go  out?  What  is  implied 
by  the  order  in  which  they  are  ex- 
tinguished? Ascertain  the  effect  of 
introducing  fresh  air  by  means  of  a 

tube  reaching  to  the  top  of  the   standard,  and  connected  to 

a  bellows. 


FIG.  101. 


HEAT. 


139 


231.  Exercise.  —  Test  different  parts  of  the  schoolroom 
for  carbonic  acid. 

Prepare  a  number  of  litres  of  lime-water  by  stirring  quicklime 
in  distilled  water,  and,  after  standing  a  few  hours,  filtering 
it  through  porous  paper  (Fig.  102).  Select  a  clear  white  glass 
bottle,  holding,  when  full,  10J  fluid  ounces  of  water.  Dry  it 
thoroughly,  and  fill  it  with  the  air  to  be  tested  by  taking  the 
bottle  to  that  part  of  the  room,  and  sucking  out  the  air  in  it  by 
means  of  a  glass  tube.  Avoid  breathing  through  the  tube  into 
the  bottle.  Now  introduce  half  a  fluid 
ounce  of  clear  lime-water,  cork  the  bottle, 
and  shake  vigorously  for  several  seconds. 
If,  after  the  air-bubbles  have  disappeared, 
the  liquid  is  not  clear,  the  air  examined 
contains  at  least  0.06  per  cent  of  car- 
bonic acid.  If  an  eight-ounce  bottle 
is  used,  turbidity  indicates  at  least  0.08 
per  cent.  A  six-and-a-half-ounce  bottle 
will  show  0.1  percent;  a  five-and-a-half- 
ounce  bottle  will  show  0.12  per  cent.  If 
one  ounce  of  lime-water  is  used,  a  seven 

ounce  bottle  will  show  0.2  per  cent;  a  five-ounce  bottle  will 
show  0.3  per  cent ;  a  four-ounce  bottle  will  show  0.4  per  cent. 
Compare  the  air  of  a  room  which  has  recently  been  occupied 
by  a  large  class  with  that  of  one  which  has  been  vacant  for 
several  hours.  Test  the  air  at  the  top,  at  the  middle,  and  at 
the  bottom  of  the  room. 

Breathe  through  a  glass  tube,  holding  the  end  in  a  vessel  of 
lime-water,  and  note  the  effect.  Also  let  a  candle  burn  for  a 
short  time  in  a  large  bottle,  then  remove  it,  pour  in  lime-water, 
shake  the  bottle,  and  mark  the  effect.  Account  for  the  air  of 
rooms  becoming  vitiated. 


FIG.  102. 


140  PRACTICAL   PHYSICS. 


V.    EXPANSION    BY    HEAT. 

232.  Apparatus.  —  Heavy   Wire,  Pyrometer,   Metal  Ball, 
Caliper,  Compound  Bar,  Florence  Flasks,  Glass  Tubing,  Ther- 
mometer, etc. 

233.  Exercise.  —  Ascertain  whether  heat  affects  the  length 
/ \         of  a  wire. 

f     \J  Bend  a  thick  brass  or  iron  wire  about  25  cm. 

long  into  a  rectangular  figure  ;   cut  out  of  one  side 
a  piece  5  cm.  long,  and  adjust  the  link  so  that 
this   piece   fits   exactly   the   place   from    which   it 
was  taken  when  at  the  temperature  of  the   room 
(Fig.  103).     The  ends  of  the  parts  must  be  planes 
perpendicular  to  the  axis  of  the  wire.     Hold  the 
FIG.  103.       straight  piece  with  a  pair  of  tongs  in  a  flame,  and, 
when  hot,  try  to  insert  it  in  its  place  in  the  link.     Inference. 

234.  Exercise.  —  Determine  the  coefficient  of  expansion  of 
a  metallic  rod. 

Employ  an  apparatus  of  the  form  shown  in  Fig.  104,  in 
which,  by  means  of  a  compound  lever,  the  expansion  is 
magnified.  HK  is  a  copper  tank  30  cm.  long,  5  cm.  deep, 
and  3  cm.  wide.  This  rests  on  the  base  of  the  instrument,  and 
is  prevented  from  moving  towards  K  by  a  brace  L.  In  this 
tank,  place  the  rod,  rest  it  on  short  pieces  of  glass  tubing 
placed  across  the  bottom.  One  end  of  the  rod  must  press 
firmly  against  the  end  K  of  the  tank ;  the  other  end  must 
press  against  the  flat  vertical  rod  D  which  is  soldered  at  right 
angles  to  the  rod  BF  supported  by  the  block  P,  and  free  to 
turn  about  its  axis  without  play.  The  bearing  at  A  is  made 
in  two  parts,  and  works  in  a  groove  in  the  rod  BF,  preventing 


HEAT. 


141 


motion  lengthwise.  The  pointer  CE  is  soldered  at  right  angles 
to  BF  at  B,  the  part  BE  being  heavy  enough  to  cause  D  to 
press  firmly  against  the  end  of  the  rod  in  the  tank.  The  ex- 
pansion of  the  rod  will  cause  the  pointer  to  move  over  the 
scale  M,  and  the  space  traversed  divided  by  the  ratio  of  BC  to 
the  arm  D  will  be  the  expansion  of  the  rod.  It  should  be 


FIG.  104. 

observed  that  the  arm  D  extends  from  the  centre  of  the  end  of 
BF  to  the  point  of  contact  of  the  upper  edge  of  the  rod  in  the 
tank  with  D. 

To  use  the  apparatus,  measure  accurately  the  rod  by  laying 
it  on  a  finely  divided  steel  scale,  then  place  it  in  the  tank  and 
record  the  reading  of  the  pointer  and  the  temperature  of  the 
rod.  Now  fill  the  tank  with  boiling  water,  and  again  record 
the  reading  of  the  pointer  and  the  temperature  of  the  rod  or 
water.  From  these  data  compute  the  rod's  change  in  length, 
and  also  its  change  per  unit  of  length  for  one  degree. 


235.    Exercise.  —  Determine  the  effect  of  heat  on  a  metal 
ball. 

Adjust  a  pair  of  calipers  so  that  an  iron  or  brass  ball  will 


142  PRACTICAL   PHYSICS. 

just  pass  between  the  points.  Again  caliper  the  ball  after  it 
has  stood  for  a  few  minutes  in  hot  water.  What  fact  regarding 
the  effect  of  heat  on  substances  is  shown  by  this  experiment 
different  from  that  shown  in  the  last  experiment?  Compute 
the  change  in  volume  per  degree  from  the  change  in  diameter. 

236.  Exercise.  —  Select  two  pieces  of  brass  tubing  about 
8  cm.  long  each,  such  that  one  will  just  telescope  the  other. 
Fit  to  each  a  wooden  handle.     Heat  the  smaller  tube  in  a  gas- 
flame,  and  try  to  insert  it  within  the  larger  one.     Heat  both 
tubes,  and  then  try  to  insert  one  within  the  other.     Inference. 

237.  Exercise.  —  Fasten  together  by  rivets,  at  intervals  of 
2  cm.,  a  strip  of  sheet-iron,  and  one  of  copper  or  brass,  each 
15  cm.  long  and  2  cm.  wide.     Place  this  bar  on  the  supports 
A  and  B  of  the  apparatus  shown  in  Fig.  36.     Place  a  spirit- 
lamp  beneath  the  centre  of  the  bar.     What  is  implied  by  the 
movement  of  the  indicator  ?     Ascertain  the  effect  of  placing  ice 
on  the  upper  side  of  the  compound  bar. 

238.  Exercise.  —  Determine   the   effect   of    heat  on   the 
volume  of  a  liquid. 

Fit  a  perforated  cork  to  a  Florence  flask,  and  insert  a  glass 
tube  about  30  cm.  long,  just  reaching  through  the  cork.  Fill 
the  flask  and  part  of  the  tube  full  of  water,  excluding  all  air- 
bubbles.  The  cork  and  tube  must  fit  water-tight.  Place 
the  apparatus  on  the  sand-bath  of  the  iron  stand.  Mark  the 
position  of  the  water  in  the  tube.  Apply  heat,  and  note 
the  effect.  Inference. 

239.  Exercise.  —  Determine  the  coefficient  of  expansion  of 
a  liquid. 


HEAT.  143 

Close  one  end  of  a  glass  tube  15  cm.  long  and  about  5  mm. 
in  diameter,  by  heating  the  end  in  a  gas-flame.  Select  one  of 
uniform  bore.  Fill  the  tube  part  full  of  some  liquid,  as  water, 
alcohol,  glycerine,  ether,  or  naphtha,  and  then  tie  it  to  a 
chemical  thermometer,  so  that  the  thermometer-scale  may  be 
used  in  measuring  the  liquid  in  the  tube.  Support  the  appara- 
tus in  a  beaker  of  ice-water,  and,  when  it  has  acquired  the 
temperature  of  the  water,  ascertain  the  length  of  the  liquid 
column  in  terms  of  the  spaces  of  the  attached  thermometer- 
scale.  Then  plunge  the  apparatus  into  a  vessel  of  hot  water, 
and  note  the  thermometer  reading,  and  the  length  of  the  liquid 
column  after  the  liquid  has  ceased  rising  in  the  tube.  The  part 
of  the  tube  containing  the  liquid  must  be  kept  in  the  water  so 
that  all  the  liquid  may  be  at  the  same  temperature.  Compute, 
from  the  data,  the  expansion  per  unit  of  volume  for  one  degree, 
neglecting  the  effect  of  the  heat  on  the  capacity  of  the  tube. 

240.  Exercise.  —  Determine  the   effect   of    heat  on   the 
volume  of  air. 

Procure  a  heavy  glass  tube  about  30  cm.  long  and  2  mm. 
internal  diameter,  one  end  terminating  in  a  bulb  of  about 
5  cm.  diameter.  A  small  Florence  flask  closed  with  a  good 
cork,  through  which  passes  a  glass  tube,  will  make  a  fair 
substitute.  Support  the  tube  in  a  vertical  position,  with  the 
end  dipping  into  a  shallow  vessel  of  colored  water.  Apply 
heat  to  the  bulb  by  either  a  gas-flame,  or  by  pouring  on  hot 
water.  Note  the  effect.  Inference. 

241.  Exercise.  —  Determine  the  coefficient  of  expansion  of 
air. 

Procure  a  glass  tube  about  20  cm.  long  and  1  mm.  internal 
diameter.  Introduce  into  it  an  index  of  mercury  5  mm.  long 


144  PRACTICAL   PHYSICS. 

by  plunging  it  into  a  bottle  of  mercury,  and  then  holding  the 
finger  firmly  over  the  outer  end  of  the  tube  as  you  remove  it 
from  the  bottle.  By  inclining  the  tube,  move  the  index  along 
to  the  middle  of  the  tube,  and  then  close  one  end  of  the  tube 
by  holding  it,  in  a  horizontal  position,  in  a  gas  or  alcohol 
flame.  Tie  the  tube  to  a  chemical  thermometer  so  that  the 
thermometer-scale  may  be  used  as  one  of  equal  parts  in 
measuring  the  length  of  the  confined  air-column  in  the  tube. 
Place  the  apparatus  in  melting  ice,  and  determine  the  length  of 
the  air-column  when  the  thermometer-reading  is  zero.  Before 
taking  the  readings,  tap  the  tube  with  the  finger  to  facilitate 
the  movement  of  the  mercury  index.  Now  place  the  apparatus 
in  a  vessel  of  water  so  arranged  that  the  temperature  can  be 
increased  at  pleasure,  and  determine  the  length  of  the  air- 
column  for  10°  C.,  20°  C.,  30°  C.,  etc.  A  long  shallow  dish 
should  be  employed  in  order  that  the  apparatus  may  be  placed 
in  nearly  a  horizontal  position  to  remove  the  pressure  on  the 
air  produced  by  the  index.  Such  a  dish  can  be  easily  made 
out  of  sheet-lead,  closing  the  joints  with  plaster-of-Paris.  Heat 
the  tube  by  pouring  hot  water  into  the  dish.  Compute, 
from  the  data,  the  expansion  per  degree  of  the  air  per  unit 
of  volume  at  0°  C.,  between  0  degree  and  10  degrees,  10 
degrees  and  20  degrees,  20  degrees  and  30  degrees,  etc., 
neglecting  the  errors  arising  from  the  effect  of  heat  on  the 
volume  of  the  tube,  and  from  the  lack  of  uniformity  in  the  bore 
of  the  tube. 

242.  Exercise.  —  Fit  a  perforated  cork,  through  which 
passes  a  glass  tube,  to  a  test-tube.  As  a  test-tube  will  stand 
but  little  pressure,  soft  and  elastic  corks  must  be  employed. 
Fill  the  tube  with  water,  recently  boiled  to  expel  the  air, 
half-way  up  the  inserted  tube.  Pack  the  apparatus  in 


HEAT.  145 

finely  broken  ice,  and  watch  the  water-column  for  some 
time.  Remove  from  the  ice,  and,  with  as  little  delay  as 
possible,  plunge  the  tube  into  hot  water,  recording  the  effect 
on  the  column.  Inference. 

243.  Exercise.  —  Close  one  end  of  a  piece  of  lead  pipe 
about  30  cm.  long  and  15  mm.  in  diameter  by  flattening  it,  on 
an  anvil,  by  a  blow  from  a  hammer.     To  the 

other  end,  fit  a  perforated  cork,  through  which 
passes  a  glass  tube  about  20  cm.  long.      Bend 
the  lead  into  a  coil,  the  plane  of  which  is  per- 
pendicular to  the  glass  tube  (Fig.  105).      Now 
fill  the  apparatus  with  water  till  it  stands  at  a 
height  of  4  or  5  cm.  in  the  glass  tube.      Care 
must  be  taken  to  exclude  all  air-bubbles  from 
the  coil.     Then  pack  the  apparatus  in  a  freezing 
mixture  made  of  three  parts  of  pounded  ice,  and       ."   FlG  105 
one  of   common  salt.      Mark  the  level  of   the 
water  in  the  tube  when  first  placed  in  the  freezing  mixture. 
Observe    the    change   in   level    during   the   following   twenty 
minutes.      Explain. 
» 

244.  Exercise.  —  Prepare   an   apparatus   similar   to  that 
used  in  Art.  242.      Introduce  several  pieces  of  dry  ice,  then 
fill  the  apparatus  with  kerosene  till  the  column  reaches  within  a 
few  centimetres  of  the  top  of  the  tube.     Observe  the  change 
of  level  as  the  ice  melts.     Measure  the  amount  of  change  of 
volume ;   measure  the  amount  of  water  produced  by  the  ice. 
From  these  data,  compute  the  density  of  ice. 


146 


PRACTICAL   PHYSICS. 


VI.  THERMOMETBY. 


245.  Apparatus.  —  Thermometer,  Funnel,  Florence  Flasks, 
Air-Pump,  Condenser,  Test-Tubes,  etc. 

246.  Exercise.  —  Test   the   accuracy   of   the   location   of 
the    freezing    and     the    boiling    points    on    a    thermometer- 
stem. 

To  ascertain  if  the  zero-point  is  accurately  located,  support 
the  thermometer  in  a  burette-holder,  and  pack  around  the  bulb 

pounded  ice  as  far  up  the 
stem  as  the  zero -point. 
The  vessel  containing  the 
ice  should  have  a  hole  in 
the  bottom  for  drainage. 
A  common  funnel  will  an- 
swer (Fig.  106).  Wash  the 
ice  thoroughly  before  using, 
so  that  the  melting-point 
will  not  be  interfered  with 
by  the  presence  of  foreign 
substances.  After  the  ther- 
mometer has  remained  a 

FIG.  106.  few  minutes  in  the  melting 

ice,  observe  the  reading  of 

the  thermometer,  using  a  magnify  ing-glass  to  estimate  fractions 
of  a  degree. 

To  test  the  accuracy  of  the  location  of  the  boiling-point, 
fit  into  a  wide-mouthed  Florence  flask  a  large  glass  tube,  as 
a  lamp-chimney,  placing  candle-wick  around  the  base  of  the 
tube,  so  that  steam  from  the  water  in  the  flask  escapes  only 


HEAT. 


147 


from  the  top  (Fig.  107).  Hang  the  thermometer  within  this 
tube,  with  the  bulb  2  or  3  em.  above  the  water  in  the  flask, 
and  the  boiling-point  on  the  stem  just  above 
the  top  of  the  tube.  On  boiling  the  water 
in  the  flask,  the  mercury-column  is  enveloped 
in  steam,  and  will  be  heated  quite  uniformly. 
After  the  lapse  of  several  minutes,  the  ap- 
paratus having  time  to  become  thoroughly 
heated,  read  the  height  of  the  mercury- 
column,  and  also  observe  the  barometric 
pressure.  As  the  boiling  -  point  is  affected 
by  changes  in  the  atmospheric  pressure,  to 
obtain  the  true  boiling-point  for  the  pressure 
at  the  time  of  the  experiment,  apply  the 
formula  t  =  100°  +  0°. 0375  (b  —  760),  in 
which  b  is  the  observed  barometric  reading 
expressed  in  millimetres. 

The  record  may  be  kept  as  follows  :  — 


FIG.  107. 


Freezing-point.  .  .  . 
True  boiling-point  .  . 
Boiling-point  observed . 


Error  of  instrument    .     . 

,  as  computed  for  pressure  of  mm. 

.    Error  of  instrument 


247.  Exercise.  —  Compare  the  temperature  of  boiling  water 
with  that  of  the  steam  given  off. 

Boil  some  water  in  a  flask.  Compare  the  reading  of  the 
thermometer  when  suspended  within  the  flask,  with  the  bulb 
about  two  centimetres  above  the  boiling  water,  with  that  when 
the  bulb  is  in  the  water.  Ascertain  the  effect  of  placing 
rough  pieces  of  glass  or  stone  in  the  flask.  Account  for 
the  difference. 


148  PRACTICAL   PHYSICS. 

248.  Exercise.  —  As  in  Art.  246',  locate  the  freezing-point 
on   the   thermometer-stem.      Now  hold   the   thermometer   for 
some  moments  in  boiling  water,   and  then  replace  it  in  the 
vessel  containing  the  melting  ice,  observing  again  the  freezing- 
point.     Account  for  the  difference. 

249.  Exercise.  —  Fill  a  vessel  of  about  one  litre  capacity 
half  full  of  cold  water.      Pour  into  it  nearly  as  much  more 
boiling  water,  letting  the  stream  strike  a  floating  cork  to  break 
the  fall.      Then   observe  the  temperature  at  the  top,  at  the 
bottom,  and  midway.     Now  stir  the  water  with  the  thermom- 
eter,  and  again  observe  the  temperature.      Account   for  the 
differences.      What   precaution  does  this  experiment  suggest 
should  be  taken  in  obtaining  the  true  temperature  of  a  liquid? 

250.  Exercise.  —  Assuming  that  one  thermometer  is  cor- 
rect, compare  a  second  one  with  it,  and  make  out  a  table  of 
corrections  to  be  applied  to  its  readings. 

Suspend  the  two  instruments  side  by  side  with  the  two  bulbs 
on  the  same  level.  Pack  the  bulbs  in  melting  ice,  and  record 
the  reading  of  each.  On  removing  the  ice,  place  beneath  the 
thermometers  a  beaker  of  water  so  arranged  that  its  temperature 
can  be  varied  at  pleasure  by  introducing  ice  or  applying  heat. 
Beginning  with  ice-water,  apply  heat,  stirring  constantly  with 
a  glass  rod,  and  record  the  readings  of  the  thermometers,  as 
they  hang  with  their  bulbs  immersed  in  the  water,  for  every 
change  of  10  degrees  in  the  standard,  till  the  boiling-point  is 
reached.  Conclude  the  observations  by  returning  the  standard 
to  the  melting  ice,  and  recording  the  reading.  Correct  the 
standard  by  the  deviation  of  this  last  reading  from  zero. 
Reduce  all  the  readings  to  the  same  thermometric  scale,  and 
obtain  the  differences  between  corresponding  ones.  These 


HEAT. 


149 


differences  will   be  the  corrections  to  be  applied  to  the  ther- 
mometer under  examination  to  make  its  readings  standard. 
Enter  results  as  follows  :  — 

Standard 0°,  10°,  20°,  30°,  40°,  50°,  60°,  70°,  80°,  etc. 

Standard  corrected  ....    

The  one  being  tested   .     .     . 

Keduced  to  scale  of  standard,  

Corrections  to  be  applied      . 

251.  Exercise.  —  Determine  the  general  effect  of  changes 
in  the  atmospheric  pressure  on  the  boiling-point. 

Fill  a  small  beaker  half  full  of  water,  and  heat  it  over  a  lamp 
till  it  nearly  reaches  the  boiling-point.  Take  the  temperature, 
and  then  place  the  beaker  under 
the  receiver  of  an  air-pump.  As 
you  exhaust  the  air,  note  from 
time  to  time  the  temperature  of  the 
boiling  water  as  shown  by  a  ther- 
mometer suspended  m  it,  at  the 
same  time  reading  the  pressure- 
gauge  of  the  pump.  Inference. 

Try  alcohol,  ether,  naphtha,  etc. 

252.  Exercise.  —  Fill  a  round- 
bottomed   Florence  flask  half  full 
of  water,  and  heat  it  over  a  lamp. 
After  the  boiling  has  continued  for 

some  minutes,  and  the  air  has  been  expelled,  remove  the  flask 
from  over  the  lamp,  cork  tightly,  support  it  in  an  inverted 
position  (Fig.  108)  on  a  ring  of  the  iron  stand,  and  pour  over 
it  cold  water.  Account  for  the  result. 


FIG.  108. 


150  PRACTICAL  PHYSICS. 

253.  Exercise.  —  Determine   the   melting-points    of   such 
substances  as  tallow,  lard,  paraffine,  beeswax,  etc. 

Fill,  by  suction,  with  the  melted  substance,  a  capillary  glass 
tube  having  thin  walls,  and  close  the  end  by  fusing  it  in  a  lamp. 
On  cooling,  you  will  have  a  fine  opaque  thread  of  the  substance 
in  the  tube.  Fasten  this  tube  alongside  the  thermometer  so 
that  the  bulb  and  the  substance  to  be  melted  will  be  side  by 
side.  Place  a  small  glass  beaker  nearly  full  of  water  on  the 
sand-bath  over  the  lamp.  As  the  water  approaches  the  melting- 
point  of  the  substance,  stir  it  gently  with  the  thermometer, 
watching  closely  for  any  change  in  the  appearance  of  the 
contents  of  the  tube.  On  melting,  it  loses  its  opacity;  and, 
just  as  soon  as  that  change  is  observed,  the  reading  of  the 
thermometer  must  be  taken.  Now  let  the  water  cool,  and 
record  the  temperature  at  which  opacity  returns.  Repeat  the 
experiment  several  times,  and  use  the  average  of  the  results. 

Suitable  capillary  tubes  can  be  easily  made  by  drawing  out, 
in  a  flame,  a  piece  of  soft  glass  tubing  till  the  diameter  is  about 
one  millimetre. 

254.  Exercise.  —  Determine  the  boiling-point  of  a  liquid, 
as  ether,  naphtha,  alcohol,  turpentine,  etc. 

Fit  to  a  test-tube  of  25  mm.  diameter  a  cork  with  two 
holes.  In  one  of  these  openings,  insert  a  thermometer,  and, 
in  the  other,  a  glass  tube  bent  at  right  angles  to  serve  as  an 
escape  for  the  vapor  of  the  liquid  to  be  tested  (Fig.  109). 
Fill  the  test-tube  one-third  full  of  the  liquid,  and  insert  the 
cork,  with  the  thermometer-bulb  two  centimetres  above  the 
liquid.  Apply  heat,  and,  on  vapor  escaping  freely  from 
the  bent  tube,  take  the  reading  of  the  thermometer.  If  the 
vapor  of  the  liquid  is  combustible,  apply  the  heat  by  means 
of  an  oil  or  water  bath. 


HEAT.  151 

Why  not  have  the  thermometer-bulb  in  the  liquid  ?  Try  it, 
comparing  results  with  those  obtained 
by  the  above  process.  Repeat  the 
experiment  with  the  thermometer  in 
the  liquid,  having  first  placed  in  the 
test-tube  some  fragments  of  some 
substance  not  acted  on  by  the  liquid. 
Inference. 

For  most  liquids,  the  temperature 
increases  0°.0375  C.  for  an  increase  of 
one  millimetre  in  the  atmospheric 
pressure.  Hence,  to  reduce  the  tem- 
perature of  the  boiling-point  obtained 
above  to  that  for  a  pressure  of  760 
mm.,  add  to  it  0°. 0375 (760  —  6),  in 
which  b  is  the  barometric  pressure 

at   the  time  when  the  observation  was  made  on  the  temper- 
ature. 

255.  Exercise.  —  Determine  the  boiling-point  of  a  satu- 
rated solution  of  some  substance,  as  common  salt,  saltpetre, 
etc. 

Proceed  as  in  the  last  experiment.  The  thermometer-bulb 
must  be  in  the  liquid.  Why?  Pieces  of  broken  glass,  or  some 
substance  on  which  the  liquid  does  not  act,  must  be  placed  in 
the  tube.  Why? 

256.  Exercise.  —  Separate  a  mixture  of  two  liquids  having 
different  boiling-points,  as  alcohol  and  water. 

Set  up  an  apparatus  like  that  shown  in  Fig.  110.  In  the 
first  flask,  put  the  mixed  liquids.  This  flask  is  connected  to 
the  second  one  by  a  bent  tube  of  glass,  and,  in  a  similar 


152 


PRACTICAL   PHYSICS. 


FIG. 110. 


manner,  the  second  one  is  joined  to  the  third.  The  first  flask 
is  directly  over  the  lamp,  the  second  one  stands  on  a  water- 
bath,  and  the  third  one  stands  in  a  vessel  of  cold  water  to  keep 

it  at  a  low  temper- 
ature. The  liquid 
in  the  first  flask  is 
made  to  boil  gently, 
.while  that  in  the 
second  one  is  kept 
at  a  temperature 
intermediate  be- 
tween the  boiling- 
points  of  the  two 
liquids,  a  condition 
easily  determined 

by  having  a  thermometer  inserted  through  the  cork  into  the 
flask.  After  a  quantity  of  liquid 
has  been  collected  in  the  third 
flask,  examine  it  to  ascertain 
whether  the  experiment  has  been 
successful. 

A  very  convenient  form  of 
condenser  is  shown  in  Fig.  Ill, 
known  as  Liebig's.  It  con- 
sists of  a  large  tube  kept  filled 
with  cold  water  flowing  from 
some  convenient  reservoir, 
through  which  passes  the  deliv-  FlG- 11L 

ery-tube  from  the  flask  containing  the  liquids  to  be  separated. 
The  cold  water  enters  the  enveloping- tube  at  the  lower  end, 
and  escapes  from  the  upper  end. 


HEAT. 


153 


VII.    RADIANT    HEAT. 


FIG. 112. 


257.  Apparatus.  —  Air-Thermometer,  Leslie's  Cubes,  Flor- 
ence Flasks,  Differential  Thermometer,  etc. 

258.  Exercise.  —  Determine   how   the   temperature   of   a 
substance  affects  its  power  to  radiate  heat. 

Construct  of  tin  or  copper  a  cubical  box  one 
decimetre  on  each  edge,  with  an 
opening  in  one  side  for  the  intro- 
duction of  water  (Fig.  112) .  Fill 
it  with  water,  bring  its  tempera- 
ture to  10°  C.,  and  place  it  at 
a  distance  of,  say,  3  cm.  from  a 
Differential,  or  Air,  Thermome- 
ter (Fig.  113),  observing  the  effect.  Raise 
the  temperature  to  20°  C.,  and  again  read 
the  thermometer.  Similarly  test  30°  C., 
40°  C.,  etc.  Compare  the  indications  of  FIG.  11:3. 

the  air-thermometer  with  the  readings   of   the  mercurial  one 
in  the  tank  to  see  if  there  is  any  law  connecting  the  two. 
All  air-currents  must  be  carefully  excluded. 

259.  Exercise.  —  Ascertain  how  distance  affects  the  inten- 
sity of  radiant  heat. 

Construct  of  tin  or  copper  a  tank  5  cm.  thick  by  50  cm.  square. 
Fill  this  with  boiling  water,  and  place  it  at  a  distance  of  a  few 
centimetres  from  the  face  of  a  Thermopile  (Fig.  114),  having 
a  conical  mouth-piece  to  concentrate  the  heat  rays  on  the 
face.  Observe  the  deflection  of  the  galvanometer  connected 
with  the  thermopile.  Test  the  effect  of  increasing  the  distance 


154 


PRACTICAL   PHYSICS. 


of  the  tank  from  the  thermopile.  Is  the  surface  which  sends 
its  heat  to  the  pile  the  same  for  all  distances  of  the  tank? 
How  does  increasing  the  distance  of  the  pile  from  the  tank 
affect  the  area  of  the  surface  radiating  its  heat  to  the  pile? 
What  law  for  intensity  of  radiant  heat  can  be  inferred  from  the 
results  ? 

The  greatest  distance  that  the  tank  should  be  placed  from 
the  pile  is  that  at  which  the  sides  of   the  conical  reflector, 


FIG. 114. 

on  being  extended,  just  touch  the  edges  of  the  face  of  the 
tank.  A  sensitive  air-thermometer  can  be  substituted  for 
the  thermopile  by  adapting  to  it  a  funnel-shaped  reflector 
such  as  accompanies  the  pile,  supporting  it  in  a  burette- 
holder. 


260.  Exercise.  —  Employing  the  apparatus  of  the  last 
experiment,  place  a  large  sheet  of  cardboard  between  the  tank 
of  water  and  the  thermometer,  and  record  the  effect  on  the 
latter.  What  inference  as  to  direction  of  radiation  can  be 
made? 


HEAT.  155 

26L  Exercise.  —  Ascertain  if  air  is  essential  to  the  trans- 
mission of  radiant  heat. 

Fit  a  cork  with  two  holes  to  a  large  Florence  flask.  Insert  a 
thermometer  in  one  of  these  openings  so  that  the  bulb  is  near 
the  centre  of  the  flask.  In  the  other  opening,  fit  a  glass  tube, 
connecting  it  by  rubber  tubing  to  a  good  air-pump.  Exhaust 
the  air  as  complete!}7  as  possible,  record  the  reading  of  the  ther- 
mometer, then  plunge  the  flask  into  hot  water,  and  again  read 
the  thermometer.  Ascertain  how  much  the  thermometer  would  be 
affected  if  the  air  were  not  exhausted  from  the  flask.  Inference. 

262.  Exercise.  —  Determine  the  law  for  the  reflection  of 
heat. 

Place  a  tank  like  the  one  employed  in  Art.  258,  filled  with 
hot  water,  on  a  proper  support,  adjusting  the  height  to  that 


FIG.  115. 

of  the  bulb  of  a  differential  thermometer.  Half-way  between 
Jie  thermometer  and  the  face  of  the  tank,  place  a  mirror  hori- 
zontally. Between  the  mirror  and  the  tank,  support  a  sheet  of 
cardboard  in  which  a  hole  3  cm.  in  diameter  has  been  cut  at 
the  point  where  a  line  joining  the  centre  of  the  face  of  the  cube 
and  the  centre  of  the  mirror  intersects  it  (Fig.  115).  What  must 


156 


PRACTICAL   PHYSICS. 


be  the  course  of  the  heat  rays  which  reach  the  thermometer? 
Ascertain  if  moving  either  the  radiator  or  the  thermometer 
affects  the  readings  of  the  thermometer.  What  law  expresses 
the  facts  observed? 

Ascertain  if  different  kinds  of  reflectors  are  equally  good. 

Test  the  effect  of  fineness  of  polish. 

Test  the  effect  of  increasing  the  size  of  the  incident  angle. 

263.  Exercise.  —  Compare  the  absorptive  powers  of  differ- 
ent substances. 

Coat  with  lamp-black  one  of  the  bulbs  of  a  differential  ther- 
mometer by  mixing  the  lamp-black  with  thin  shellac  varnish. 


FIG.  116. 

Place  the  blackened  bulb  in  the  focus  of  a  concave  reflector 
such  as  is  frequently  placed  behind  wall-lamps  (Fig.  116).  At 
a  short  distance  in  front  of  the  reflector,  place  the  cubical  tank 
of  Art.  258,  filled  with  hot  water.  Compare  the  effects  of  the 
heat  on  the  plain  bulb  and  the  blackened  one. 

Try,  in  succession,  the  following  substances  as  coverings  for 
one  of  the  bulbs :    India-ink,  tin-foil,  foil  of  other  metals,  etc. 


HEAT.  157 

Arrange  the  substances  tried,  in  the  order  of  their  absorptive 
power  as  shown  by  these  experiments. 

A  differential  thermometer,  which  will  serve  for  these  experi- 
ments, may  be  made  as  follows  :  — 

Take  two  small  flasks,  and  join  them  by  a  stout  glass  tube 
about  30  cm.  long  and  1  mm.  bore,  with  its  ends  bent  at  right 
angles.  Seal  the  flasks  with  wax  to  make  them  air-tight  after 
introducing  within  the  tube  two  or  three  drops  of  colored 
water.  Attach  a  scale  of  equal  parts  to  the  horizontal  portion 
of  the  connecting-tube,  and  mount  the  apparatus  on  a  support. 

A  simple  way  of  comparing  the  absorbing  power  of  substances 
is  the  following  :  — 

Cut  two  pieces  of  bright  tin  plate  10  cm.  square.  Saw  in  a 
narrow  board  two  slits  10  cm.  apart,  and  mount  the  plates  in 
them,  having  first  coated  the  inner  face  of  one  of  them  with  the 
substance  to  be  tested.  Stick  with  wax,  using  as  little  as 
possible,  balls  of  equal  size  on  the  outside  of  each  at  about  the 
centre  of  the  face.  Now  place  a  hot  iron,  as  a  soldering-iron, 
midway  between  the  two  plates.  The  better  absorbent  will  be 
indicated  by  the  melting  of  the  wax  holding  the  ball. 

264.  Exercise.  —  Fill  the  chemical  tank  (Fig.  234)  with 
alum-water,  place  it  between  the  sun  and  a  large  reading-glass, 
and  focus  the  rays  on  a  sheet  of  paper.     Compare  the  effect 
with  that  obtained  when  the  alum- water  is  omitted.     Try  the 
effect  of  a  solution  of  iodine  in  carbon  disulphide. 

265.  Exercise.  —  Ascertain  if  the  radiating  surface  affects 
the  rate  of  cooling. 

Take  two  tanks  similar  to  that  of  Art.  258,  and  blacken  the 
faces  of  one  with  lamp-black,  leaving  the  other  bright.  Fill 
each  with  water  at,  say,  80°  C.  ;  insert  in  each  a  thermometer, 


158  PRACTICAL   PHYSICS. 

and  record  the  readings  every  five  minutes  for  half  an  hour. 
Inference. 

Two  bottles  of  the  same  shape  and  size  may  be  used  as 
substitutes. 

266.  Exercise.  —  Compare   the   radiating   power  of   sub- 
stances. 

Using  the  apparatus  of  Art.  265,  coat  one  face  of  the  tank 
with  lamp-black,  a  second  with  white  lead,  a  third  with  white 
paper,  and  the  fourth  with  cotton  cloth.  Fill  the  tank  with 
boiling  water,  and  compare  the  radiating  power  of  the  four 
faces  by  observing  the  effects  produced  on  the  thermometer  as 
each  face  is  turned  successively  toward  it  for  five  minutes. 
The  initial  temperature  of  the  water  in  the  tank  must  be  the 
same  for  each  face. 

Four  equal  bottles  coated  with  the  above  substances  respec- 
tively may  be  used  as  substitutes. 

A  radiometer  may  be  substituted  for  the  thermometer  in 
many  of  these  experiments  in  radiant  heat,  the  intensity  of 
radiation  being  indicated  by  the  speed  with  which  the  vanes 
rotate. 

267.  Exercise.  —  Determine  if  the  rate  of  cooling  of  a 
body   is   affected    by   the   amount   by   which   its   temperature 
exceeds  that  of  the  surrounding  air. 

Take  a  cylindrical  tin  can  of  about  one  litre  capacity,  such 
as  is  used  in  preserving  fruit,  remove  one  end  by  unsoldering 
it,  and  fit  to  it  a  wooden  cover,  through  the  centre  of  which  is 
a  small  hole  of  sufficient  size  to  admit  the  bulb  of  a  thermometer 
(Fig.  117).  Blacken  thoroughly  the  inside  of  the  can,  as  well 
as  the  under  side  of  the  cover,  by  holding  it  in  the  smoke  from 
burning  gum-camphor.  Select  a  thermometer  having  a  large 


HEAT. 


159 


bulb  as  the  object  whose  rate  of  cooling  is  to  be  studied.  Slide 
over  its  stem  a  cork  selected  to  fit  the  hole  in  the  cover  of  the 
can,  that  the  thermometer  may  be  supported  with  its  bulb  at 
about  the  centre  of  the  vessel.  The  tin  can  is  designed  to 
exclude  air-currents  from  the  cooling  body.  To  maintain  the 
surrounding  air  at  a  practically  constant  temperature,  sink  the 
vessel  nearly  to  its  top  in  a  large  vessel  of  water.  Take 
the  temperature,  which  will  be  that 
of  the  chamber,  then  introduce 
within  the  chamber  the  thermom- 
eter heated  to,  say,  80°  C.,  by  ci 
dipping  it  into  hot  water,  care- 
fully drying  it  with  a  cloth  before 
putting  it  in  place.  Record  the 
reading  of  the  thermometer  for 
every  half-minute.  In  a  parallel 
column,  write  the  differences  be- 
tween these  readings  and  the  tem- 
perature of  the  water.  These  will 
be  the  excess  of  the  temperature  of  the  object  over  that  of  the 
surrounding  air  for  each  half -minute.  In  a  third  parallel 
column,  write  the  number  of  degrees  the  temperature  of  the 
object  has  fallen  each  half-minute.  Finally,  ascertain  the  ratio 
of  the  excess  of  the  temperature  of  the  cooling  body  above  the 
temperature  of  the  chamber,  for  each  half-minute,  to  the  fall  of 
temperature  during  each  corresponding  half-minute,  and  place 
the  results  in  a  fourth  parallel  column.  A  comparison  of  these 
ratios  will  enable  you  to  decide  whether  the  rate  of  cooling  is 
in  any  way  connected  with  the  temperature  of  the  surrounding 
medium. 


FIG.  117. 


160  PRACTICAL  PHYSICS. 

VIII.    CALORIMETBY. 

268.  Apparatus.  —  Beakers,  Thermometer,  Florence  Flasks, 
Metal  Balls  of  different  substances  and  of  the  same  diameter, 

etc. 

269.  Exercise.  —  Show  that  the  capacity  of  water  for  heat 
is  nearly  constant ;  that  is,  the  heat  required  to  raise  a  given 
quantity  of  water  a  given  number  of  degrees  in  one  part  of  the 
thermometric  scale  is  able  to  raise  the  same  quantity  nearly  the 
same  number  of  degrees  in  any  other  part  of  the  scale. 

Balance  two  thin  glass  beakers  of  about  one  litre  capacity 
each,  on  the  opposite  pans  of  a  balance,  and  pour  into  each 
400  grammes  of  water.  Let  one  be  brought  to  the  temperature 
of  the  room,  and  the  other  heated  to  about  60°  C.  Replace 
the  beakers  on  the  balance,  and  adjust  the  weights  which  have 
been  disturbed  by  evaporation.  Now  take  the  temperature  of 
each,  observing  the  heated  one  last.  Why?  Then,  without 
delay,  pour  the  heated  one  into  the  other,  stirring  constantly 
with  the  thermometer  for  a  few  seconds,  and  record  the  temper- 
ature of  the  mixture.  The  difference  between  the  temperatures 
of  the  mixture  and  the  hot  water  will  be  the  number  of  degrees 
lost  by  the  hot  water.  Likewise  the  difference  between  the 
temperatures  of  the  mixture  and  the  cold  water  will  be  the  num- 
ber of  degrees  gained  by  the  cold  water.  The  average  of  the 
initial  temperatures  will  nearly  equal  that  of  the  mixture  ;  the 
discrepancy  being  due  to  the  heat  absorbed  by  the  cold  beaker, 
that  lost  by  radiation,  and  possibly  that  the  amount  of  heat 
required  to  raise  cold  water  one  degree  is  different  from  that 
required  to  produce  the  same  change  in  hot  water. 

Repeat  the  experiment,  with  the  change  that  the  cold  water 
is  poured  into  the  hot,  to  ascertain  how  much  the  heat  in  the 


HEAT.  161 

warmer  beaker  influences  the  result.  Then  the  heat  in  the  glass 
will  go  to  raise  the  temperature  of  the  cold  water,  and  hence 
increase  the  temperature  of  the  mixture. 

In  subsequent  experiments,  methods  of  correcting  for  absorp- 
tion and  radiation  are  given.  These  corrections  carefully 
applied  to  this  problem  have  shown  that  the  capacity  of  water 
for  heat  is  not  strictly  constant,  but  increases  slightly  with  the 
temperature. 

270.  Exercise.  —  Mix  unequal  quantities  of  water  at  differ- 
ent temperatures,  and  ascertain  the  temperature  of  the  mixture. 
Compare  the  result  with  that  obtained  by  computation  on  the 
supposition  that  all  the  heat  lost  by  the  hot  water  went  to 
the  cold  water. 

To  compute  the  temperature,  divide  the  total  number  of  heat 
units  in  the  two  quantities  of  water  by  the  total  quantity  of 
water. 

271.  Exercise.  —  Determine    the    water-equivalent    of    a 
vessel ;   that  is,  find  how  much  water  will  equal  it  in  capacity 
for  heat. 

Dry  the  vessel  thoroughly,  and  let  it  come  to  the  temperature 
of  the  room,  which  will  be  indicated  when  a  thermometer 
suspended  in  it  registers  the  same  as  when  without  it.  Then 
pour  in  it  a  known  quantity  of  water,  as  .4  kg.,  at  a  known 
temperature,  say,  40°  C.,  and  record  the  temperature  after  the 
lapse  of  about  thirty  seconds.  The  fall  in  temperature  is  due 
to  heat  having  been  absorbed  by  the  vessel,  and  to  radiation, 
while  pouring  in  the  water  and  stirring.  This  may  be  allowed 
for  as  follows  :  Before  pouring  the  water  into  the  vessel,  ascer- 
tain the  fall  of  temperature  in  one  minute,  then  observe  the  fall 
in  one  minute  following  the  period  of  thirty  seconds  allowed  for 


162  PRACTICAL   PHYSICS. 

the  heat  to  be  communicated  to  the  vessel.  Then  the  radiation 
rate  may  be  taken  as  the  average  of  these  two  losses.  One- 
half  of  this  will  be  the  loss  from  radiation  during  the  thirty 
seconds,  and  will  be  the  amount  to  be  added  to  the  observed 
temperature  of  the  water  in  the  vessel  to  give  the  correct 
temperature  for  the  water,  and  hence  of  the  vessel.  The 
number  of  calories  Of  heat  consumed  by  the  vessel  will  be 
the  loss  of  temperature  on  the  part  of  the  water,  times  the 
amount  of  water.  This  divided  by  the  gain  of  the  vessel  will 
give  the  number  of  calories  required  to  change  the  temperature 
of  the  vessel  one  degree,  and  hence  will  be  the  number  of 
kilogrammes  of  water  to  which  the  vessel  is  equivalent. 

272.  Exercise.  —  Determine  the  thermal  capacity  of  a 
substance,  as  lead,  copper,  etc. 

Make  a  loose  coil  of  a  known  weight  of  the  metal  in  sheet 
form,  and  suspend  it,  by  a  thread,  in  boiling  water  for  a 
sufficient  time  to  acquire  the  temperature  of  the  water.  The 
temperature  of  the  boiling  water  must  be  observed.  Why? 
Pour  into  a  beaker,  whose  water-equivalent  has  been  deter- 
mined as  in  Art.  271,  a  known  weight  of  water  of  the  tem- 
perature of  the  room,  and  of  sufficient  amount  to  cover  the  coil 
entirely  when  placed  within  it.  Now  transfer  to  it  the  heated 
coil,  stir  the  water  around  thoroughly  with  a  thermometer,  and 
record  the  reading  when  it  ceases  to  rise,  and  also  the  time 
occupied  in  thus  equalizing  the  temperatures.  Keep  up  the 
stirring  for  one  minute  longer,  that  the  effect  of  radiation  may 
be  observed.  Half  of  this  loss  multiplied  by  the  time  occu- 
pied in  securing  equalization  must  be  added  to  the  observed 
temperature,  to  give  the  correct  temperature  produced  in  the 
water  by  the  heated  coil.  Now  add  to  the  weight  of  water 
used,  the  water-equivalent  of  the  beaker,  and  multiply  this  by 


HEAT.  163 

the  gain  in  temperature  to  obtain  the  number  of  calories  of  heat 
imparted  by  the  coil  to  the  water  and  beaker.  This  product 
divided  by  the  number  of  degrees  lost  by  the  coil  will  give  its 
capacity  for  heat. 

273.  Exercise.  —  Compare,  by  Tyndall's  method,  the  ther- 
mal capacities  of  several  metals. 

Make  a  ball  out  of  each  of  the  metals  lead,  tin,  zinc,  bismuth, 
antimony,  etc.,  by  the  aid  of  a  pair  of  large  bullet-moulds,  and 
an  iron  spoon  in  which  to  melt  the  metal.  Reduce  them  to 
the  same  weights  by  cutting  off  a  part  of  the  ball.  Solder  a 
fine  wire  handle  to  each.  Mould, 
in  a  shallow  pan,  a  cake  of  wax 
about  5  mm.  thick.  Support  the 
cake  in  a  horizontal  position  by 
its  edges.  Heat  the  balls  in  boil- 
ing water  till  they  have  acquired 
the  temperature  of  the  water.  FIG  ug 

Place  them  simultaneously  on  the 

wax,  several  centimetres  apart,  and  observe  the  time  occupied 
by  each  in  melting  through  the  cake  (Fig.  118).  Some  of  the 
balls  may  not  get  through ;  in  that  case,  the  depth  the  ball 
melts  into  the  cake  must  be  noted.  The  drop  of  water  adhering 
to  each  ball  must  be  removed  before  placing  the  ball  on  the 
wax  cake.  The  handles  should  be  attached  at  the  point  where 
the  weight-adjustment  was  made,  so  that  like  surfaces,  in  every 
case,  will  be  in  contact  with  the  wax.  Only  approximate 
results  can  be  secured  by  this  method. 

274.  Exercise.  —  Determine  the  specific  heat  of  a  liquid. 
First  Method.  — Make  a  loose  coil  of  some  metal,  as  lead, 

whose   specific   heat   is   known,    and  then,   proceeding   as   in 


^^^^ 

FTfa 


164  PRACTICAL   PHYSICS. 

Art.  272,  find  its  thermal  capacity  with  reference  to  the  liquid  in 
question  by  substituting  the  liquid  for  the  water.  The  quotient 
of  the  heat  capacity  when  compared  with  water,  by  that  when 
compared  with  the  liquid,  will  give  the  thermal  capacity  of  the 
liquid  with  reference  to  water. 

Second  Method.  —  Procure  two  test-tubes  of  the  same  size  ; 
in  one  of  them  pour  a  few  grammes  of  water,  and,  in  the 
other,  an  equal  volume  of  the  liquid  under  examination.  In 
each  test-tube,  insert  a  thermometer ;  then  place  the  tubes 
in  a  vessel  of  water,  at,  say,  70°  C.,  as  indicated  by  a  third 
thermometer,  and  note  the  time  required  for  the  contents  of  the 
tubes  to  acquire^ that  temperature.  As  these  substances  differ 
in  density,  it  will  be  necessary  to  reduce  these  times  to  those 
for  equal  weights  by  dividing  each  by  the  density  of  the  corre- 
sponding liquid.  The  ratio  of  these  times  will  be  the  specific 
heat  of  the  liquid.  Compare  the  results  given  by  this  method, 
with  those  given  by  the  first. 

Try  turpentine,  ether,  kerosene,  benzine,  glycerine,  etc. 

275.  Exercise.  —  Determine  the  latent  heat  of  water  ;  that 
is,  find  the  number  of  calories  of  heat  disappearing  during  the 
melting  of  one  kilogramme  of  ice. 

Pour  into  a  beaker  a  known  quantity  of  water,  say  500 
grammes,  and  raise  its  temperature  to,  say,  70°  C.  Set  the 
beaker  on  a  board,  and  observe  the  fall  in  temperature  during 
one  minute.  Now  add  ice  in  small  pieces  till  about  200 
grammes  have  been  introduced,  constantly  stirring  the  water 
with  the  thermometer.  Each  piece  of  ice  should  be  wiped  with 
a  dry  cloth  before  putting  it  in  the  beaker,  to  avoid  introducing 
any  water  in  the  liquid  form.  The  time  occupied  in  putting  in 
the  ice  should  be  as  short  as  possible.  As  soon  as  the  ice  is 
melted,  take  the  temperature  of  the  water,  and  record  the  time 


ttEAf.  165 

occupied.  Also  obtain  the  fall  due  to  radiation  during  the 
next  minute.  The  amount  of  ice  introduced  is  the  increase  in 
weight  of  the  beaker  and  contents.  The  following  example 
will  show  the  method  of  making  the  computation :  — 

Amount  of  water  in  beaker 500  grammes. 

Temperature  of  water 75°  C. 

Fall  in  temperature  during  one  minute 1|°  C. 

Temperature  of  water  taken  as  soon  as  ice  melted    .  32°  C. 

Fall  in  temperature  during  next  minute |°  C. 

Time  required  to  melt  ice 3  minutes. 

Amount  of  ice  introduced 179  grammes. 

Water-equivalent  of  beaker  previously  determined  .  34  grammes. 

Data  corrected  for  radiation  and  absorption  :  — 

Amount  of  water,  500  +  34  =  534  grammes. 
Temperature  of  water  before  introducing  ice,  73^°  C. 
Temperature  of  water  after  introducing  ice,  32  +  s(  *  2    2J  =  35°  C. 

.534(734  —  35)  =  20.559  calories  of  heat  consumed; 

.179  X  35  =    6.265  calories  of  heat  consumed  in  raising  the  ice 
froinO0  to  35°; 

.  • .     20.559  —  6.265  =  14.294  calories  of  heat  consumed  in  melting .  179  kg. 

of  ice, 

.-.     14.294  ~r    .179  =  79.9  calories  of  heat  consumed  in  melting  1  kg.  of 

ice. 

276.   Exercise.  —  Determine  the  latent  heat  of  steam. 

Fit  to  a  Florence  flask  of  about  one  litre  capacity  a  delivery- 
tube  of  the  form  shown  in  Fig.  119.  Fill  the  flask  half  full  of 
water,  and  support  it  on  the  iron  stand.  The  delivery-tube 
should  reach  nearly  to  the  bottom  of  a  beaker  containing  a 


166 


PRACTICAL   PHYSICS. 


known  quantity  of  water,  say  400  grammes,  at  the  temperature 
of  the  room.      Apply  heat  to  the  flask,   and,   as  soon  as  a 

strong  jet  of  steam  issues  from 
the  delivery-tube,  let  it  enter  the 
water  in  the  beaker.  Stir  the  water 
constantly  and  gently  with  the  ther- 
mometer ;  and,  when  the  tempera- 
ture has  risen  a  certain  number  of 
degrees,  as  20°  C.,  record  the  time 
occupied,  and  also  the  fall  from 
radiation  during  the  next  minute. 
Then  ascertain  the  increase  in 
weight,  and  also  the  temperature  of 
steam.  The  following  example  will 
show  the  method  of  making  the  computation  :  — 


FIG. 119. 


Amount  of  water  in  beaker 400  grammes. 

Water-equivalent  of  beaker  previously  determined .  34  grammes. 

Temperature  of  water  in  beaker 21°.  75  C. 

Temperature  of  water  after  steam  ceases  to  enter    .  41°.  75  C. 

Loss  in  one  minute  from  radiation 0°.25  C. 

Time  occupied  in  admitting  steam 4.25  minutes. 

Amount  of  steam  introduced 14  grammes. 

Temperature  of  steam 99°.  25  C. 

Temperature  of  water  in  beaker  corrected  for  radiation, 

25 
41.75  +  V  X  4.25  =  42°.28  C. 

Zi 

Amount  of  water  corrected  for  beaker-equivalent,  434  grammes. 

.434  X  20.53  —  8  91  calories  of  heat  imparted  to  the  water. 
.014(99.25  —  42.28)  =    .8  calories  of  heat  derived  from  the  water  produced 
by  the  steam  in  condensing  and  cooling  from 
99°.  25  C.  to  42.28  C. 

.*.    8.91  —  .8  =  8.11  calories  of  heat  derived  from  .014  kg.  of  steam 
condensing  to  water  at  the  boiling-point. 


HEAT.  167 

Hence 

8.11  -r  .014  =  579.3  calories  of  heat  latent  in  1  kg.  of  steam. 

It  will  be  observed  that  the  large  piece  of  tubing  inserted  in 
the  delivery-tube  will  retain  the  water  produced  by  steam 
condensing  before  reaching  the  water  in  the  beaker.  To  admit 
this  would  introduce  serious  error.  Why? 

IX.    ARTIFICIAL    COLD. 

277.  Exercise.  —  Dissolve  in  three  parts,  by  weight,  of 
water  not  warmer  than  10°  C.,  a  mixture  of  two  parts  of  pul- 
verized ammonium  nitrate  and  one  part -of  ammonium  chloride. 
Stir  the  mixture  with  a  test-tube  containing  water,  observing 
the  reading  of  a  thermometer  placed  in  the  tube.      Account 
for  the  low  temperature. 

278.  Exercise.  —  Dissolve  common  salt  in  water,  and  see 
if  it  affects  the  temperature  of  the  water  in  any  way.      Try 
potassium  nitrate,  ammonium  nitrate,  etc.     Try  some  substance 
not  having  a  crystalline  character,  as  dextrine,  gum-arabic,  etc. 
Account  for  the  difference  in  the  results. 

279.  Exercise.  —  Tie  a  piece  of  cotton-wool  about  the  bulb 
of  a  mercurial  thermometer.      Wet  the  wool  with  ether,  and 
note  the  effect.     Explain. 

280.  Exercise.  —  Pour  water  at  the  temperature  of  the 
room  into  a  porous  cup,  such  as  is  used  in  the  construction  of 
galvanic  batteries.     A  new  unglazed  flower-jar  will  answer  the 
purpose  if  the  drainage-hole  is  closed  up.     Take  the  tempera- 


168  PRACTICAL   PHYSICS. 

tu re  every  five  minutes  for  half  an  hour,  and  also  that  of  the 
room  at  the  same  time.     Account  for  the  difference. 

281.  Exercise.  —  Place   a   bell-jar   on   the  table    of    the 
air-pump,   observe   closely  the   degree   of  transparency,   then 
exhaust  the  air,  watching  for  any  change  in  the  appearance  of 
the  jar.     Now  admit  the  air,  introduce  a  thermometer,  take  the 
temperature,  and,  after  exhausting  the  air,  again  take  the  tem- 
perature.     Why  is  it  lower?      Account  for  the   phenomenon 
seen  during  the  first  exhaustion.     What  applications  can  you 
find  in  the  theory  of  clouds,  of  the  truth  brought  out  in  this 
experiment  ? 

282.  Exercise.  —  As  in  Art.  278,  dissolve  sodium  sulphate 
in  water,  determining  the  effect  on  the  temperature.      Now 
prepare  a  saturated  solution  of  sodium  sulphate  by  dissolving 
a  few  grammes  of  the  substance  in  an  equal  weight  of  hot 
water.     Set  the  solution  aside  in  a  vessel  to  cool,  having  first 
poured  a  thin  layer  of  oil  over  the  top.     If  not  disturbed,  it 
will  cool  to  the  temperature  of  the  room  without  crystallizing. 
After  waiting  long  enough  to  be  certain  that  the  solution  has 
reached  the  temperature  of  the  room,  introduce  a  thermometer, 
and  observe  the  effect.     Explain. 

Try  sodium  acetate  in  the  same  manner. 

283.  Exercise.  —  Test   some    of    the    following   freezing- 
mixtures  :  — 

1st,  Common  salt,  by  weight,  one  part ;  snow  or  pounded 
ice,  two  parts.  The  temperature  will  sink  to  —20°  C. 

2d,  Common  salt,  by  weight,  five  parts ;  ammonium  nitrate, 
five  parts  ;  snow  or  pounded  ice,  twelve  parts.  The  temperature 
will  sink  to  -31°  C. 


HEAT.  169 

3d,  Crystallized  calcium  chloride,  by  weight,  two  parts ; 
snow  or  pounded  ice,  two  parts.  The  temperature  will  sink 
to  -40°  C. 

4th,  Sodium  phosphate,  by  weight,  nine  parts ;  dilute  nitric 
acid,  four  parts.  The  temperature  will  sink  to  —29°  C. 

5th,  Sodium  sulphate,  by  weight,  six  parts ;  ammonium 
nitrate,  five  parts  ;  dilute  nitric  acid,  four  parts.  The  temper- 
ature will  sink  to  —26°  C. 

In  these  mixtures,  the  substances  are  supposed  to  be  at  the 
temperature  of  10°  C.  If,  however,  they  are  previously  cooled 
down,  a  lower  temperature  still  can  be  obtained  in  most  cases. 


170  PRACTICAL  PHYSICS. 


CHAPTER   V. 

MAGNETISM    AND    ELECTRICITY. 
I.    MAGNETS.  —  POLARITY.  —  INDUCTION. 

284.  Apparatus,  —  Bar-Magnets,  Needles,  Thin  Plates  of 
Different  Substances,  Short  Rod  of  Soft  Iron,  Carpet-Tacks, 
etc. 

285.  Exercise.  —  Touch  one  end  of  a  bar-magnet  to  a  pile 
of  carpet- tacks,  and  record  the  effect.    Try  the  other  end  of  the 
magnet.     Count  the  number  of  tacks  adhering  in  each  case,  and 
obtain  the  average  of  a  number  of  trials.     Inference.     Ascer- 
tain if  any  piece  of  steel  will  affect  the  tacks  in  the  same  way. 

Make  a  paper  stirrup,  place  the  bar-magnet  in  it,  and  suspend 
the  bar-magnet  by  a  thread,  thus  giving  the  magnet  freedom  of 
motion.  Now  bring  near  each  end,  in  succession,  an  iron  nail. 
Repeat  the  experiment,  the  nail  and  magnet  having  changed 
places.  Does  the  magnet  attract  the  nail,  or  does  the  nail 
attract  the  magnet? 

Magnets  for  the  purpose  of  this  experiment,  as  well  as  the 
following  ones,  may  be  made  by  stroking,  from  end  to  end, 
and  always  in  the  same  direction,  large  steel  nails,  or  short 
steel  rods,  with  one  pole  of  an  electro-magnet  (Art.  382). 

286.  Exercise.  —  Float   a   common   darning-needle   on  a 
piece  of  cork  in  a  glass  vessel  of  water,  and  ascertain,  by 
making  several  trials,  if,  after  coming  to  rest,  it  points  in  any 


MAGNETISM  AND  ELECTRICITY.  171 

one  way  in  preference  to  another.  Now  stroke  the  needle, 
from  end  to  end,  with  one  pole  of  a  magnet,  and  repeat  the 
tests.  Inference. 

287.  Exercise.  —  Magnetize  a  large  sewing-needle  by  strok- 
ing it  a  few  times  with  one  pole  of  a  magnet.     Pull  a  silk  fibre 
several  centimetres  long  out  of  silk  floss,  by  untwisting  it,  and 
attach  it,  by  a  very  little  wax,  to  the  needle,  so  that,  on  holding 
it  up,  the  needle  will  take  a  horizontal  position.     Cement  the 
other  end  of  the  fibre  to  one  end  of  a 

small  glass  tube  passing  through  the  cen- 
tre of  a  cork.  Fit  this  cork  to  the  top  of 
a  large  lamp-chimney  or  bottle.  The 
length  of  the  fibre  should  be  such  as  to 
bring  the  needle  within  half  a  centimetre 
of  the  base.  This  instrument  will  serve 

FIG. 120. 

as  a  magnetoscope.     A  pocket-compass, 

or  a  magnetic  needle,  mounted  as  in  Fig.  120,  may  be  used 

instead. 

Magnetize  a  large  darning-needle  by  stroking  the  half  toward 
the  point  with  the  south-seeking  pole  of  a  magnet,  and  the 
other  half  with  the  north-seeking  pole.  Ascertain  which  is 
the  north-seeking  pole  of  the  needle  as  in  the  last  experiment. 
Now  bring  its  north-seeking  pole  near  that  pole  of  the  magneto- 
scope,  and  record  the  effect.  Try  the  other  pole.  What  law 
seems  to  govern  the  action  of  magnets  toward  each  other  ? 

288.  Exercise.  —  Hold  the  north-seeking  pole  of  a  strong 
magnet  near  the   north-seeking   pole  of  a  feebly  magnetized 
needle,   and   ascertain   if   the  effect  is  in   harmony  with   the 
law  of  magnetic  action.     Now  re-examine  the  polarity  of  the 
small  needle.     Inference. 


172  PRACTICAL   PHYSICS. 

289.  Exercise.  —  Ascertain  if  a  strong  permanent  magnet 
will  attract  iron-filings  or  tacks  through  thin  plates  of  mica, 
wood,  paper,  glass,  copper,  zinc,  iron,  etc. 

290.  Exercise.  —  Bend  a  strip  of  heavy  sheet-iron,  15  cm. 
by  5  cm.,  into  a  ring.     Suspend,  by  a  thread,  from  a  wooden 
support,  a  small  piece  of  iron,  and  adjust  it  to  hang  at  the 
centre  of  this  hollow  cylinder  as  it  rests  on  the  table.     Now 
hold,  opposite  the  ball  of  iron  on  the  outside  of  this  cylinder, 
a  strong  magnet,  and  compare  the  effect  on  the  ball  with  that 
produced  if  the  ring  is  removed  and  the  magnet  is  held  at  the 
same  distance  as  before.     Try  a  brass  or  zinc  ring,  and  see  if 
the  effect  is  the  same. 

291.  Exercise.  —  Hang  as  many  tacks  as  possible  from  the 
pole  of  a  magnet  supported   in   a  horizontal   position  above 
the  table,  using  a  clamp  for  the  purpose.      Hold  up  to  it  a 
sheet  of  paper  carrying  carpet-tacks,   and  notice  how  many 
adhere.     Now  place  a  second  magnet  beneath  this  one,  so  that 
its  opposite  pole  is  exactly  under  the  one  supporting  the  tacks, 
and  ascertain  if  the  power  of  the  first  magnet  to  support  tacks 
has  been  affected.     Now  place  the  magnet  so  that  like  poles 
are  opposite,  and  repeat  the  tests.     Explain. 

292.  Exercise.  —  Hold  one  end  of  a  rod  of  soft  iron  near  one 
pole  of  a  magnet,  and,  while  in  that  position,  dip  the  other  end  of 
the  rod  into  iron-filings.     Record  the  result.    Test  the  soft-iron 
bar  for  polarity  while  in  this  position,  using  a  pocket-compass 
for  the  purpose.     Note  the  effect  of  removing  the  magnet. 

Vary  the  experiment  by  holding  the  magnet  near  to  the 
middle  of  the  rod,  and  testing  the  whole  rod  with  iron-filings. 
Also  test  for  polarity. 


MAGNETISM  AND   ELECTRICITY.  173 

Arrange  two  such  rods  end  to  end  along  on  a  table,  and  not 
quite  in  contact.  Near  one  end  of  the  row,  hold  a  strong  magnet. 
Test  the  last  one  of  the  row  with  iron- filings.  If  placed  with 
its  end  projecting  over  the  edge  of  the  table,  a  dish  of  filings 
can  be  held  to  it  without  trouble.  Also  test  each  end  of  these 
bars  with  a  compass-needle  to  ascertain  their  polarity. 


II.    NATURE    OF    MAGNETISM. 

293.  Apparatus.  —  Steel    Bar,    Magnet,    Needles,    Steel- 
Pilings,  etc. 

294.  Exercise.  —  Ascertain  if  it  sensibly  affects  the  weight 
of  a  bar  of  steel  to  magnetize  it. 

295.  Exercise.  —  Take  a  piece  of  No.  16  iron  wire  about  30 
cm.  long,  anneal  it  carefully  by  heating  it  red-hot,  and  letting  it 
cool  very  slowly.     Turn  at  right  angles  one  centimetre  at  each 
end  for  convenience  in  holding.     Now  stroke  it  carefully  with 
a  magnet  several  times,  and  test  its  power  to  lift  iron  filings. 
Then  give  the  wire  a  sudden  twist,  and  again  test  it. 

Magnetize  a  knitting-needle  ;  test  its  power  to  pick  up  small 
iron  tacks ;  then,  holding  one  end  firmly,  make  the  needle 
vibrate  by  plucking  the  free  end,  and  again  test  its  power  to 
lift  small  iron  tacks. 

296.  Exercise.  —  Magnetize  a  needle,  or  a  piece  of  steel 
wire,  and  dip  one  end  into  a  dish  of  small  iron  tacks,  noticing 
the  number  adhering  as  you  lift  it  out.    With  a  pair  of  crucible 
tongs,  hold  the  needle  in  a  flame  till  red-hot,  and  then  plunge 
it  quickly  into  the  tacks,  and  notice  if  it  picks  up  as  many  as 
before.     Test  again  after  the  needle  has  become  cold. 


174  PRACTICAL   PHYSICS. 

Vary  the  experiment  by  ascertaining  if  a  magnet  will  attract 
a  small  nail  when  it  is  red-hot.  Also  vary  the  experiment  by 
letting  a  heated  steel  needle  cool,  having  placed  it,  when 
red-hot,  in  a  line  between  the  opposite  poles  of  two  magnets. 

From  the  nature  of  heat,  what  does  this  experiment  suggest 
regarding  magnetism  ? 

297.  Exercise.  —  Magnetize  a  knitting-needle,  and  roll  it 
in  iron-filings,  recording  the  result.      Now  break  the  needle 
into  two  equal  pieces,  and  test  them.     Break  these  pieces,  and 
test  them.     Why  do  not  filings  adhere  at  the  centre?     What 
view  of  the  nature  of  magnetism  is  here  supported  ? 

298.  Exercise.  —  Fill  a  glass  tube  1  cm.  in  diameter  and 
10  cm.  long  with  very  short  pieces  of  steel  wire,  or  with  steel 
filings,  closing  the  ends  with  a  cork.     Stroke  the  tube  with  a 
powerful  magnet,  and  test  it  for  polarity  by  holding  its  ends  in 
succession  near  one  pole  of  the  magnetoscope.     Now  shake  up 
the  contents  of  the  tube  thoroughly,  and  again  test  its  polarity. 
Inference. 

The  coercive  force  can  be  imitated  by  mixing  a  little  oil  with 
the  filings.  It  will  be  found  more  difficult  to  magnetize  and 
demagnetize  the  tube. 

III.    THE    MAGNETIC    FIELD. 

299.  Apparatus.  --  Magnets,     Short     Magnetic    Needle 
mounted,   Magnetoscope,   etc. 

300.  Exercise.  —  Map  out  the  magnetic  field  of  a  magnet. 
Place  a  short  bar-magnet  beneath  a  stiff  sheet  of  writing- 
paper  supported  on  two  wooden  bars  as  thick  as  the  magnet, 


MAGNETISM  AND  ELECTRICITY.  175 

and  sift  iron-filings  evenly  over  it  from  a  thin  muslin  bag 
containing  them,  tapping  the  paper  gently  to  facilitate  the 
movements  of  the  filings.  Study  the  figures  obtained  in  this 
way  for  a  horse-shoe  magnet,  a  disk-magnet,  two  bar-magnets 
placed  parallel  to  each  other,  with  like  poles  adjacent,  and 
separated  by  about  two  centimetres  ;  two  magnets  with  unlike 
poles  adjacent,  horse-shoe  magnet  with  its  armature  on,  a 
bar-magnet  with  a  bar  of  soft  iron  near  one  of  its  poles,  an 
iron  ring  when  a  powerful  magnet  is  near  it,  a  bar-magnet  held 
vertically,  etc. 

Permanent  copies  of  these  figures  may  be  made  as  follows  :  — 

Brush  a  sheet  of  printing-paper  over  with  a  solution  of 
tannin,  and  place  it  carefully  on  the  figure  after  removing  the 
magnet.  Place  on  this  a  sheet  of  heavy  blotting-paper,  and 
apply  a  slight  pressure.  On  lifting  off  the  paper,  most  of  the 
filings  will  adhere  to  it,  and  can  be  brushed  off  when  dry, 
leaving  dark  marks  on  the  paper. 

Place  a  small  magnetic  needle  successively  in  different  parts 
of  the  magnetic  field,  as  marked  out  by  the  filings  before 
removing  the  magnet,  and  notice  its  position  with  reference 
to  the  line  of  force  passing  through  the  support. 

A  suitable  needle  may  be  constructed  as  follows  :  Straighten 
a  piece  of  watch-spring,  cut  from  it  a  lozenge-shaped  piece 
15  mm.  long,  and  drill  a  hole  1  mm.  in  diameter  through  the 
centre.  Cement,  with  a  little  wax,  a  small  cap  exactly  over 
this  hole  to  serve  as  a  bearing.  To  make  such  a  cap,  heat  the 
end  of  a  very  small  glass  tube  in  a  Bunsen  flame  till  the  glass, 
by  contracting,  closes  the  end.  Cut  off,  with  a  file,  a  piece 
about  3  mm.  long,  and  you  will  have  a  cap  with  a  smooth 
conical  hole  in  it  for  the  reception  of  the  supporting  pivot. 
For  a  pivot,  break  off  the  point  of  a  sewing-needle,  and  insert 
it  in  a  piece  of  wood  1  cm.  square  and  2  mm.  thick  for  a  base. 


176  PRACTICAL   PHYSICS. 

If  the  needle  is  not  level  after  magnetization,  adjust  it  with  a 
little  wax. 

301.  Exercise.  —  Represent,  by  a  curve,  the  change  in  the 
magnetic  strength  as  you  go  from  the  poles  of  a  magnet  to 
the  centre. 

Magnetize,  as  uniformly  as  possible,  a  heavy  knitting-needle. 
This  is  best  done  by  the  method  known  as  Divided  Touch.  It 
consists  in  fixing  the  needle  lengthwise  between  the  opposite 
poles  of  two  permanent  magnets,  and,  while  under  their  induc- 
tion, stroke  the  needle,  each  half,  with  the  pole  of  another 
magnet  of  the  same  name  as  the  corresponding  inducing  pole, 
the  stroking-magnets  being  held  in  the  hands  at  an  angle  of 
about  30  degrees  with  the  needle.  The  stroking  must  begin  at 
the  centre  of  the  bar,  the  poles  being  lifted  at  the  ends,  and 
brought  back  in  an  arch  to  the  centre.  The  stroking  should 
be  repeated  on  the  opposite  side  of  the  needle. 

A  Coulomb's  magnetoscope  will  be  required  for  this  experi- 
ment. To  construct  one,  magnetize  to  saturation  a  small 
cylinder  of  glass-hard  steel  about  10  mm.  long  by  5  mm.  in 
diameter.  Suspend  this,  by  a  silk  fibre,  in  a  glass  tube  about 
15  cm.  long  set  into  a  wooden  base.  A  wire  hook  sliding 
through  a  cork  fitted  to  the  tube  will  serve  to  support  the  fibre. 
The  magnet  is  cemented  in  a  wire  stirrup,  and  should  hang 
about  midway  between  the  ends  of  the  tube.  To  prevent  it 
from  swinging,  connect  it,  by  a  second  fibre,  to  a  small  lead 
disk  resting  on  the  floor  of  the  tube. 

Place  the  magnetoscope  on  the  table,  and,  by  means  of  a 
magnet,  produce  a  small  displacement  of  the  magnetoscope- 
needle  in  order  to  set  it  in  vibration  through  a  small  arc. 
Ascertain  the  number  of  oscillations  made  in  thirty  seconds, 
while  vibrating  under  the  influence  of  the  earth  alone,  averaging 


MAGNETISM  AND   ELECTRICITY.  177 

at  least  three  trials.  Now  support  the  magnetized  knitting- 
needle  in  a  vertical  position,  bring  its  centre  near  the  magneto- 
scope  and  in  the  magnetic  meridian.  As  before,  ascertain  the 
number  of  vibrations  made  by  the  magnetoscope-needle  in 
thirty  seconds,  being  careful  to  set  it  vibrating  through  an  arc 
of  the  same  size  as  before. 

In  a  similar  way,  test  the  ends  of  the  magnet,  and  four  or 
more  places  between  the  centre  and  the  ends.  Care  must  be 
taken  not  to  vary  the  distance  between  the  magnet  and  the 
maguetoscope,  and  not  to  change  the  position  of  the  magneto- 
scope  on  the  table.  The  bringing  of  like  poles  together  must 
be  avoided  so  that  attraction,  and  not  repulsion,  will  actuate 
the  instrument.  The  position  of  the  points  on  the  magnet, 
which  were  tested,  must  be  known  relatively  to  the  length  of 
the  magnet. 

Now  square  the  number  of  vibrations  in  .each  case,  and 
subtract  the  square  of  the  number  representing  the  magnetism 
of  the  earth.  The  numbers  thus  obtained  represent  the  relative 
magnetic  intensities  at  these  points,  since  the  attractive  force 
varies  as  the  square  of  the  number  of  vibrations.  Draw  a 
straight  line  10  cm.  long  to  represent  the  magnet.  At  points 
situated  like  those  tested  on  the  magnet,  erect  perpendiculars. 
Make  the  one  at  the  plus  pole  2  cm.  long  to  represent  the 
magnetic  intensity  at  that  point,  and  give  the  others  lengths 
proportional  to  the  numbers  just  obtained.  Through  the 
extremities  of  these  lines,  sketch  a  curve,  and  you  have  a 
graphic  representation  of  the  change  in  magnetic  intensity  as 
you  go  from  the  middle  of  a  magnet  toward  either  end. 

302.  Exercise.  —  Proceeding  as  in  the  last  experiment, 
compare  the  strengths  of  the  north-seeking  poles  of  two  bar- 
magnets. 


178 


PRACTICAL   PHYSICS. 


303.  Exercise.  —  Proceeding  as  in  Art.  301,  determine  the 
number  of  vibrations  made  by  the  needle  of  the  magnetoscope, 
in  thirty  seconds,  when  distant  from  the  pole  of  a  magnet 
2  cm.,  3  cm.,  4  cm.,  etc.,  respectively.     Compare  the  ratios  of 
these  numbers  representing  the  strengths  of  the  magnetic  field 
at  these  distances  from  the  pole  with  the  ratios  of  the  distances. 
If  the  experiment  is  carefully  conducted,  one  set  of  ratios  will 
be  found  to  be  the  square  of  the  other  set  taken  in  an  inverse 
order.     What  law  is  supported  by  this  fact? 

304.  Exercise.  —  Determine,    from    the    law    of    inverse 
squares,  the  direction  a  magnetic  needle  will  have  when  at  rest 
in  the  neighborhood  of  a  bar-magnet. 

Magnetize  a  knitting-needle,  and  lay  it  on  a  straight  line 
drawn  on  a  sheet  of  paper,  marking  on  this  line  the  position  of 

the  poles  N  and 
S  of  the  magnet 
at  one-tenth  of  the 
length  of  the  nee- 
dle from  the  end 
(Fig.  121),  as  the 
poles  of  a  magnet 
are  not  at  its  ends. 
Xake  A  as  a  point 

FlO.  121. 


S 


in    the    magnetic 

field.  The  north-seeking  pole  of  a  magnet  at  A  would  be 
attracted  by  S  along  the  line  AS,  and  repelled  by  N  along  AN. 
Measure  AS  and  AN,  and  then  lay  off  AB  any  convenient 
number  of  centimetres,  and  AD  as  many  times  greater  than 
AB  as  AS  squared  is  greater  than  AN  squared.  Complete  the 
parallelogram  ABCD,  and  the  diagonal  AC  will  represent,  by 
its  length  and  direction,  the  magnitude  and  the  direction  of  the 


MAGNETISM  AND  ELECTRICITY.  179 

resultant  magnetic  force  at  A.  Verify  the  conclusion  by 
placing  a  short  magnet  at  A  free  to  turn,  such  as  was  employed 
in  Art.  300. 

Locate  a  number  of  these  lines  of  direction,  and  compare 
them  with  the  lines  of  force  for  the  magnet  as  marked  out 
by  the  use  of  iron-filings. 

IV.    TERRESTRIAL   MAGNETISM. 

305.  Apparatus.  —  Dipping-Needle,    Iron    Bar,    Compass, 

etc. 

306.  Exercise.  —  Determine    the    dip    of    the    magnetic 
meridian. 

Fasten,  with  a  little  wax,  a  thread  to  the  middle  of  an 
unmagnetized  knitting-needle,  finding, 
by  trial,  a  point  of  attachment  in  which 
the  needle  takes  a  horizontal  position. 
Now  stroke  the  needle  with  a  magnet, 
and  suspend  it  by  the  thread  attached. 
It  now  acts  as  if  one  end  has  become 
heavier  than  the  other.  To  obtain  ac- 
curately the  amount  of  this  dip,  a  Dip- 
ping-Needle  (Fig.  122)  will  be  needed. 

This,  when  placed  in  the  magnetic  meridian,  shows,  on  a 
graduated  arc,  the  amount  of  dip. 

307.  Exercise.  —  Procure  a  thoroughly  annealed  iron  bar 
75  cm.  long,  showing  little  or  no  polarity  when  tested  with  a 
magnetic  needle  while  the  bar  is  supported  horizontally  in  an 
east-and-west  line.     Now  support  this  bar  in  a  position  parallel 
to  that  taken  by  the  dipping-needle  of  the  last  experiment,  and 


180  PRACTICAL   PHYSICS. 

again  test  it  for  polarity.     Turn  the  bar  end  for  end,  and  again 
test  it  for  polarity.     Inference. 


V.    FRICTIONAL    ELECTRICITY. 

308.  Apparatus.  —  Glass    Rods,   Sealing-wax   Rod,  Silk, 
Flannel,  Pith-Balls,  Electroscope,  etc. 

309.  Exercise.  —  Balance  a  common  yard-stick,  or  a  strip 
of  lath,  on  the  point  of  a  needle  projecting  through  a  cork  in  a 
bottle.     Hold,  near  one  end  of  the  stick,  a  rod  of  sealing-wax 
immediately  after  rubbing  it  briskly  with  flannel.      A  rubber 
comb  or  ebonite  ruler  may  be  substituted  for  the  sealing-wax. 

Try  a  glass  tube  after  rubbing  it  briskly  with  a  piece  of  silk. 
The  tube  should  be  about  50  cm.  long  and  2  cm.  in  diameter, 
with  the  ends  rounded,  by  softening  them  in  a  gas-flame,  to 
prevent  cutting  the  fingers  when  experimenting  with  it.  The 
tube  and  the  silk  should  be  warmed  before  using.  Glass  free 
from  sodium  is  best  for  the  purpose. 

Describe  the  effects  these  objects  have  on  the  balanced  strip. 

See  if  there  is  any  connection  discoverable  between  the 
mechanical  energy  expended  in  rubbing  the  rod,  and  the  inten- 
sity of  the  state  developed  in  it. 

310.  Exercise.  —  Excite  each  of  the  various  rods  used  in 
the   last   experiment,   and   in   the   way   there   described,    and 
immediately  bring  it  near  to  a  pile  of  pith-balls  or  small  bits 
of  tissue-paper. 

The  pith-balls  can  be  obtained  from  the  common  elder,  or 
from  the  corn-stalk.  They  may  have  a  diameter  from  5  mm. 
to  1  cm.  Cut  the  pith  with  a  veiy  sharp  knife  in  order  that 
each  ball  may  have  a  smooth  surface. 


MAGNETISM  AND  ELECTRICITY. 


181 


311.  Exercise.  —  Make  a  hoop  out  of  paper,  say,  20  cm.  in 
diameter  and  8  cm.  wide.    Place  it  upon  a  table,  and  hold  a  glass 
rod  excited  by  rubbing  with  silk  a  little  below  one  extremity  of 
a  horizontal  diameter  of  the  hoop.     Do  not  let  the  hoop  touch 
the  rod,  but  keep  it  at  a  distance  of  one  or  two  centimetres 
from  its  outer  surface.     Describe  the  effect  on  the  hoop. 

312.  Exercise.  —  Determine  the  law  of  electrical  action. 
Rub  a  glass  rod  with  silk,  and  suspend  it  in  a  paper  stirrup 

(Fig.  123).  In  like  manner,  excite  a  second  glass  rod  with  as 
little  delay  as  possible, 
and  bring  it  near  one 
end  of  the  suspended 
one.  Note  the  effect. 
Now  try  two  rods  of 
sealing-wax  or  ebonite 
in  the  same  way,  and 
observe  the  effect.  Fi- 
nally, try  one'of  glass, 
and  one  of  sealing- 

•h  »• 

wax,  and  observe  their     .  FlG- 123- 

action  toward  each  other.  If  we  represent  the  electrification 
of  glass  by  +E,  and  that  of  sealing-wax  by  — E,  what  law 
expresses  the  conclusions  reached  ? 

313.  Exercise.  —  Draw  a  silk  ribbon  between  two  layers  of 
warm  flannel,  and  hold  it  near  a  wall  or  some  object.      Try 
two  strips  of  ribbon  hanging  side  by  side.     Explain. 


314.  Exercise.  —  Place  a  sheet  of  brown  paper  on  a  hot 
dry  board.  Brush  it  briskly,  for  a  few  moments,  with  a  hair 
clothes-brush.  Cut  part  of  the  paper  into  narrow  strips  free 


182 


PRACTICAL   PHYSICS. 


at  one  end,  with  a  sharp  knife,  without  touching  the  surface  of 
that  part  with  the  hand.  Observe  the  action  of  these  strips 
toward  one  another.  Explain. 

315.  Exercise.  —  Test  various  articles  found  in  the  room, 
for  electrification,  after  rubbing  them  with  either  silk,  fur,  or 
flannel. 

Select  a  Florence  flask  of  about  one  litre  capacity,  thoroughly 
clean  and  dry  it ;  fit  to  it  a  cork,  through  which  passes  a  stout 
brass  wire,  on  the  outer  end  of  which  is  a 
metal  ball  about  15  mm.  in  diameter,  or 
a  thick  brass  disk  of  the  same  diameter, 
having  the  edges  neatly  rounded  off  with  a 
fine  file  (Fig.  124).  File  the  end  of  the 
wire  within  the  flask  to  a  wedge  form, 
the  edge  having  a  thickness  of  not  over  one 
millimetre.  Cut,  out  of  thin  tin  or  alu- 
minum foil,  two  strips,  each  5  mm, 
wide  and  6  cm.  long,  and  paste  them  on 
the  faces  of  the  lower  end  of  the  wire  so 
that  they  will  hang  side  by  side.  Tin-foil 
(No.  4),  such  as  is  used  by  dentists,  makes 
excellent  strips  for  this  purpose.  Such  an  instrument  is  called 
an  Electroscope.  To  use  it,  bring  the  article  suspected  of 
being  electrified  near  the  ball  of  the  instrument ;  the  divergence 
of  the  leaves  shows  electrification. 

If  a  little  strong  sulphuric  acid  is  put  in  the  flask,  it  will 
tend  to  dry  the  air  within  it,  and  increase  the  duration  of  the 
charge. 

316.  Exercise.  —  Determine  the  kind  of  electrification  of  a 
body. 


Fift.  124. 


MAGNETISM  AND  ELECTRICITY.  183 

Charge  an  electroscope  with  the  unknown  kind  of  electrifica- 
tion, using  a  proof-plane  for  the  purpose.  A  Proof-Plane 
(Fig.  125)  is  usually  a  small  metal  disk  cemented  to  the  end  of 
a  glass  or  ebonite  rod.  A  serviceable  instrument  can  be  made 
by  cementing  a  cent,  after  filing  the  edges  smooth,  to  a  glass 
tube  about  15  cm.  long.  To  charge  the  electroscope,  slide 
the  metal  disk  of  the  proof-plane  along  the  surface  to  be 
tested,  and  then  bring  it  in  contact  with  the  electroscope-knob. 
Repeat  the  operation  till  the  ends  of  the  leaves 
are  about  1  cm.  apart.  Now  excite  strongly,  by 
friction  with  silk,  a  dry  glass  rod.  If  the  silk 
rubber  is  coated  with  amalgam  (see  Appendix, 
p.  360),  a  higher  electrification  can  be  secured. 
Charge  the  proof-plane  by  putting  it  in  contact 
with  the  rod,  and  then,  without  delay,  place  this 
charged  proof-plane  in  contact  with  the  electro- 
scope-knob. If  the  leaves  diverge  farther,  the 
object  in  question  was  positively  charged ;  if  the 
leaves  collapse,  it  was  probably  negative.  As  ^ 
increased  divergence  is  a  more  reliable  indication 
of  electrification  than  a  decreased  divergence,  in  case  of  the 
latter  occurring  it  is  best  to  repeat  the  test,  using  a  rod  of 
sealing-wax  and  flannel  in  place  of  the  glass  rod  and  the  silk. 

It  is  important  that  the  electroscope  be  not  charged  too 
highly,  as,  in  that  case,  a  decreased  divergence  might  mean 
that  the  intensity  of  the  known  charge  in  the  proof-plane  was 
less  than  that  of  the  electroscope,  and  of  the  same  kind,  thus 
introducing  doubt.  Always  charge  the  proof -plane  as  intensely 
as  possible,  in  order  that  ambiguity  may  not  arise. 

Test  the  kind  of  electrification  of  the  silk  ribbon  in  Art.  313, 
the  paper  in  Art.  314,  common  rubber  excited  by  flannel, 
glass  excited  by  flannel,  stick-sulphur  excited  by  flannel,  sul- 


184  PRACTICAL  PHYSICS. 

phur  excited  by  silk,  rubber  excited  by  silk,  sealing-wax  excited 
by  cotton,  paper  excited  by  flaimel,  etc. 

317.  Exercise.  —  Excite  a  glass  rod  by  rubbing  it  with 
silk,  keeping  the  silk  rubber  from  touching  the  hand  by  means 
of  a  square  piece  of  sheet-rubber  such  as  dentists  use.     Test 
the  silk  for  electrification.     Similarly  test  the  flannel  employed 
in  rubbing  sealing-wax,  fur  in  rubbing  any  resinous  substance, 
etc.     Inference. 

318.  Exercise.  —  Compare  the  conducting  power  of  sub- 
stances for  electricity. 

Place  one  end  of  a  thread  of  the  substance  whose  conductivity 
is  to  be  tested,  in  contact  with  the  electroscope-knob,  and  the 
other  in  contact  with  a  smooth  metallic  button  supported  on  a 
rod  of  sealing-wax.  A  thread  50  cm.  long  may  be  used  when 
possible,  and,  in  case  of  some  substances,  it  would  be  well  to 
make  it  still  longer.  Now  touch  the  button  with  a  highly 
charged  proof-plane,  and  decide,  from  the  action  of  the 
electroscope,  whether  the  substance  is  a  good  conductor,  a 
semi-conductor,  or  a  non-conductor. 

Try  silk  thread,  cotton  thread,  linen  thread,  woollen  thread, 
glass  thread,  rubber,  wood,  paper,  wire,  graphite  as  found  in  a 
lead-pencil,  any  kind  of  thread  wet  with  water,  etc. 


VI.    STATICAL    INDUCTION. 

319.  Apparatus.  —  Insulated  Metallic  Cylinders  and  Balls, 
Electroscope,  Metallic  Cylindrical  Pail,  etc. 

320.  Exercise.  —  Place  end  to  end,  and  in  contact,  two 
metallic  cylinders  about  20  cm.  long  and  4  cm.  in  diameter, 


MAGNETISM  AND  ELECTRICITY.  185 

having  rounded  ends,  each  cylinder  being  supported  on  a 
varnished  glass  rod  inserted  in  a  wooden  base  (Fig.  126). 
Wooden  cj'linders  smoothly  covered  with  tin-foil  make  a  cheap 
and  efficient  substitute,  the  foil  being  fastened  on  with  flour- 
paste.  Metallic  door-knobs  mounted  on  glass  rods  work  well. 
As  you  hold  near  one  end,  that  is,  2  or 
3  cm.  removed,  a  highly  electrified  glass 
rod,  by  means  of  a  proof-plane  and  elec- 
troscope test  the  outer  ends,  and  the 
point  of  contact,  of  the  two  cylinders 
for  electrification.  If  found  to  be  elec- 
trified, ascertain  the  kind.  Now  re- 
charge the  glass  rod  ;  and,  as  you  hold 
it  near  the  end  of  one  of  the  cylinders, 

separate  the  cylinders  by  several  centimetres.  Test  the  ends 
of  the  separated  cylinders  for  electrification,  comparing  results 
with  those  obtained  when  the  cylinders  were  in  contact. 
Explain. 

This  experiment  will  succeed  only  in  a  very  dry  atmos- 
phere. 

321.  Exercise.  —  Connect  one  end  of  the  insulated  metal- 
lic cylinder  of  the  last  experiment  with  an  electroscope  by 
means  of  a  wire,  the  ends  of  which  are  rounded,  or  bent 
around  into  a  loop  and  soldered.  Hold  an  electrified  glass 
rod  near  the  other  end  of  the  cylinder,  and  record  the  effect 
on  the  electroscope.  Before  removing  the  excited  rod,  remove 
the  wire,  handling  it  with  some  non-conductor.  If  the  wire 
rests  loosely  on  the  cylinder  and  on-  the  ball  of  the  electro- 
scope, it  can  be  lifted  off  with  a  glass  rod.  Ascertain  the 
electrical  condition  of  the  electroscope  as  well  as  of  the 
cylinder. 


186  PRACTICAL  PHYSICS. 

322.  Exercise.  —  Hold  one  finger  on  the  ball  of  an  electro- 
scope, and  bring  near  it  an  electrified  glass  rod.     Remove  the 
finger  before  taking  away  the  rod.      Determine  the  electrical 
condition    of    the    electroscope.      Try   a   rod   of    sealing-wax 
excited  b}*  flannel,  in  place  of  the  glass  rod. 

This  is  a  very  desirable  way  of  charging  an  electroscope  with 
a  known  kind  of  electricit}T.  The  intensity  of  the  charge  can 
be  varied  by  changing  the  distance  the  excited  bod}*  is  held 
from  the  ball  of  the  instrument. 

323.  Exercise.  —  Determine  how  the  amount  of  electricity 
induced    on    neighboring    conductors    compares   with   that   of 
the  inducing  body. 

Procure  a  metallic  cylindrical  pail  free  from  points,  and 
support  it  on  a  plate  of  well-dried  glass  to  insulate  it.  This 
vessel  should  have  a  depth  of  about  25  cm.  and  a  diameter  of 
about  15  cm.  It  may  be  made  of  tin  or  copper.  Connect  the 
outside,  by  a  wire,  to  the  ball  of  an  electroscope.  Suspend 
by  a  silk  thread  a  metallic  ball,  say,  5  cm.  in  diameter,  having 
a  smooth  surface  and  positively  charged,  within  the  pail. 
Notice  the  indication  of  the  electroscope.  With  a  proof-plane 
and  a  second  electroscope,  determine  the  electrical  condition  of 
the  two  surfaces  of  the  pail.  Ascertain  if  the  position  of  the 
electrified  ball  within  the  pail  in  any  way  affects  the  attached 
electroscope.  Touch  the  ball  to  the  bottom  of  the  pail,  and 
observe  if  the  electroscope  is  affected.  Now  remove  the  ball, 
and  test  it  for  electrification.  What  must  have  been  the 
amount  of  the  electricity  on  the  inside  of  the  pail  compared 
with  that  on  the  ball?  What  must  have  been  the  amount  of 
electricity  on  the  outside  of  the  pail  ? 


MAGNETISM  AND   ELECTRICITY.  187 


VII.    ELECTRICAL    DISTRIBUTION. 

324.  Apparatus.  —  Metal   Beaker,  Pane   of    Glass,  Wide 
Brass    Ring,    Electroscope,    Brass    Chain,    Insulated    Metallic 
covered  Ball,  Cylinder,  and  Cone ;  Proof-Plane,  Insulated  Metal 
Disks,  etc. 

325.  Exercise.  —  Support  on  a  dry  pane  of  glass  a  metallic 
vessel   of   about   one   litre    capacity,   free   from  sharp  edges. 
Charge  it  with  electricity  by  rubbing  an  excited  glass  rod  over 
it.     Employing  a  proof-plane  and  an  electroscope,  test  the  two 
surfaces  for  electricity.     Inference. 

326.  Exercise.  —  Bend  into  a  ring  a  heavy  strip  of  sheet 
brass  25  cm.  long  and  8  cm.  wide,  soldering  the  ends  together, 
and  filing  the  edges  round.     Suspend  from  the 

inside  surface  a  pair  of  pith-balls,  and  a  second 
pair  from  the  outside  surface.  The  inside  pair 
of  balls  should  be  at  the  centre  of  the  ring. 
Suspend  the  apparatus  by  a  silk  cord  from  a 
support.  Now  electrify,  by  friction,  a  glass 
rod,  and  rub  it  across  the  cylinder,  observing 
the  effect  on  the  pith-balls.  Inference. 

Fig.  127  shows  such  a  cylinder  mounted  on 
an  insulated  stand. 

327.  Exercise.  —  Support  the  metal  vessel 
of  Art.  325  on  a  dry  pane  of  glass,  and  connect 

its  outer  surface  with  the  ball  of  the  electroscope  by  means 
of  a  wire.  Suspend  within  the  vessel,  from  a  glass  rod, 
a  metre  or  less  of  brass  chain.  Charge  the  vessel  with  elec- 
tricity till  the  leaves  of  the  electroscope  diverge  widely ;  then 


188  PRACTICAL   PHYSICS. 

lift  up  the  chain  so  that  less  of  it  lies  piled  up  on  the 
bottom  of  the  dish,  observing  the  effect  on  the  electroscope. 
Keeping  in  mind  that  lifting  up  the  chain  practically  in- 
creases the  surface  of  the  vessel  without  decreasing  the 
quantity  of  electricity,  what  inference  can  be  drawn  regarding 
the  effect  on  potential  produced  by  changing  the  amount  of 
surface  ? 

328.  Exercise.  —  Determine  whether  the  shape  of  a.  con- 
ductor in  any  manner  affects  the  distribution  of  the  electrical 
charge. 

Cover  smoothly  with  tin-foil  a  wooden  ball  8  cm.  in  diameter, 
a  conical-shaped  piece  15  cm.  long,  with  hemispherical  ends 
5  cm.  and  1.5  cm.  in  diameter,  respectivel}',  and  a  disk  2.5 
cm.  thick  and  8  cm.  in  diameter,  the  edges  being  rounded. 
Support  each  of  these  on  a  varnished  heavy  glass  rod,  as  an 
ignition-tube,  set  into  a  suitable  base,  or  suspend  each  of  them 
by  a  silk  cord.  Now  charge  the  first  insulated  conductor  with 
electricity,  and  compare  the  relative  magnitude  of  the  charge 
at  different  parts  by  observing  how  many  charges  brought 
by  the  proof-plane  to  the  electroscope  from  one  place  are 
necessary  to  produce  the  same  amount  of  divergence  of  the 
leaves  of  the  electroscope  as  one  or  more  brought  from 
another  place.  In  like  manner,  test  the  other  conductors. 
Is  there  any  connection  between  the  electrical  density  and  the 
degree  of  curvature  of  the  surface  ?  Try  a  conductor  pointed 
at  one  end,  made  so  by  inserting  a  piece  of  needle.  Can 
you  charge  it?  Explain.  Why  avoid  points  on  electrical 
apparatus  ? 

In  applying  the  proof-plane,  always  place  its  disk  flat  against 
the  conductor  to  avoid  changing  the  shape  of  the  conductor 
under  examination. 


MAGNETISM  AND   ELECTRICITY.  189 

329.  Exercise.  —  Determine  the  effect  of  neighboring  con- 
ductors on  the  distribution  of  the  electrification  of  an  insulated 
conductor. 

Charge  with  electricity  the  insulated  cylinder  of  the  last 
experiment,  and  place  near  one  end  of  it  a  similar  conductor 
connected  by  a  wire  or  chain  with  the  gas,  water,  or  steam 
pipes  of  the  room.  Examine,  as  in  that  experiment,  the 
insulated  cylinder,  comparing  the  distribution  with  that  found 
when  there  was  no  neighboring  conductor. 

330.  Exercise.  —  Determine  whether  the  distance  of  neigh- 
boring conductors  affects  the  distribution  of  electricity  oa  an 
insulated  conductor,  and  also  whether  any  effects  are  due  to  the 
nature  of  the  medium  separating  the  electrified  body  from  these 
conductors. 

Construct  three  lead  or  brass  disks  15  cm.  in  diameter,  the 
edges  being  neatly  rounded,  and  suspend  them  by  silk  cords 
so  as  to  hang  parallel ;  or,  better  still,  mount  them  on  glass 
supports,  securing  them  to  the  glass  with  wax.  Connect  each 
outside  one  with  a  wire  to  an  electroscope.  Charge  the  middle 
one  with  known  electricity,  and  observe  the  effect  on  the 
electroscopes  when  the  disk  is  midway  between  the  two  outer 
ones.  Move  the  disk  nearer  to  one  of  the  outer  ones,  and  note 
the  effect.  Insert  a  dry  unelectrified  pane  of  glass  between 
these  two.  Try  plates  of  other  substances.  Inference. 

331.  Exercise.  —  Enclose  an  electroscope  in  a  cage  or  box 
made  of  wire-cloth.    Bring  any  electrified  object  in  contact  with 
this  wire  covering,  and  observe  the  effect  on  the  electroscope. 
Now  connect  the  cage  with  the  earth  by  leading  a  wire  from 
it   to  the  gas-pipe,   and  again   pass   electric  charges  through 
it,  observing   the  effect  on  the  electroscope.     What  method 


190  PEACTICAL   PHYSICS. 

of  protecting  buildings  from  lightning  is  suggested  by  this 
experiment  ? 

VIII.    CONDENSERS. 

332.  Apparatus.  —  Tin-Foil,  Paper,  Leyden  Jars,  Electro- 
scopes, etc. 

333.  Exercise.  —  Cut  three  pieces  of  paper  15  cm.  square, 
and  four  of  tin-foil  10  cm.  square.     Coat  the  paper  with  paraf- 
fine  or  shellac  varnish.      Arrange  these  pieces  in  a  pile  with 

the  foil  and  paper  alter- 
nating. Connect  with 
wire  the  alternate  pieces 
of  foil,  making  two 
groups  (Fig.  128).  Join 
one  of  these  to  the  prime 

FIG.  128.  conductor  of  an  electri- 

cal machine,  and  the  other  to  the  earth.  After  working  the 
machine  for  a  minute,  touch  the  wire  leading  to  the  earth  to 
the  one  leading  to  the  machine.  Explain. 

The  ends  of  the  wires  should  be  rounded.     Why?      Glass 
may  be  substituted  for  the  paper,  and  gilt-paper  for  the  foil. 

334.  Exercise.  —  Place  on   the   table  a  piece   of   tin -foil 
about  25  cm.  square,  and  connect  it  to  the  earth  by  a  wire  or 
chain.     On  this,  lay  a  pane  of  glass,  around  which  pass  two 
silk  ribbons  for  removing  the  glass  when  necessary  without 
touching  either  the  glass  or  the  foil  with  the  fingers.     On  the 
glass,  lay  a  small  piece  of  tin-foil,  and  connect  it  with  the 
electroscope   by    means    of   a   wire.      Charge    with    electricity 
the  upper  sheet  of  foil,  noticing  the  effect  on  the  electroscope. 
Now  lift  up  the  glass  plate  by  means  of  the  ribbons,  disconnect 


MAGNETISM  AND   ELECTRICITY.  191 

the  lower  piece  of  foil  from  the  earth ;  then  replace  the  glass 
plate,  all  the  time  watching  the  indications  of  the  electroscope. 
Explain. 

335,  Exercise.  —  Hold  the  ball  of  a  Leyden  Jar  (Fig.  129) 
in   contact  with  the   prime  conductor  of   an  active  electrical 
machine,  at  the  same  time  connecting  the  outer  surface  of  the 
jar  with  the  negative  conductor  of   the  machine  by 

means  of  a  wire  or  chain.     After  a  few  minutes,  the 
jar  will  have  acquired  a  maximum  charge. 
Using  a   bent  wire,  or  Jointed  Discharger 
(Fig.  130),  connect  the  two  surfaces.      If 
the  wire  is  brought  in  contact  with  the  outer 
surface  of  the  jar  first,   no  shock  will  be 
experienced    by  the    experimenter.      After 
waiting  a  few  moments,  you  may  be  able  to 
FIG.  I3o7    obtain  from  the  same  jar,  without  recharging,  a  second 
discharge  of  much  less  intensity  than  the  first,  called 
the  Residual  Charge      The  time  necessary  for  the  accumulation 
of  the  second  charge  can  be  shortened  by  gently  tapping  the  jar 
with  a  glass  or  wooden  rod.     What  change,  suggested  by  this 
experiment,  is  probably  effected  in  a  body  on  electrifying  it? 

336.  Exercise.  —  Connect   the  inner  surfaces   of   several 
Leydeu  jars  by  winding  a  brass  chain  about  the  rods  passing 
through  the  covers.     The  outer  surfaces  may  be  connected  by 
placing  the  jars  side  by  side  on  a  sheet  of  tin-foil.     Charge 
the  battery  in  the  same  manner  as  a  single  jar.     Compare  the 
intensity  of  the  charge  with  that  of  a  single  jar  by  the  length 
of  the  spark  seen  on  discharging. 

Leyden  jars  are  easily  made  out  of  candy-jars  by  coating  the 
outside  with  tin-foil  to  about  two-thirds  of  its  height,  using 


192  PRACTICAL   PHYSICS. 


thin  flour-paste  to  cause  the  foijjo_^jhere-  If  the  opening  of 
the  jar  is  large  enough,  the  inside  may  be  similarly  coated  ; 
but,  if  too  small  to  admit  the  hand,  fill  the  jar  two-thirds  full 
with  tinsel  or  crumpled  tin-foil.  Fit  to  the  jar  a  varnished 
wooden  stopper,  through  which  passes  a  heavy  copper  or  brass 
wire  connecting  with  the  inner  surface  of  the  jar  by  a  piece  of 
brass  chain.  The  outer  end  of  the  brass  rod  should  terminate 
in  a  ball.  One  cast  out  of  lead  will  answer  as  well  as  any.  All 
glass  is  not  equally  good  as  an  electric.  The  electrical  qualities 
of  a  jar  should  be  tested  before  pasting  on  the  foil,  by  tying  on 
the  outside  a  sheet  of  foil,  filling  the  inside  part  full  of  crumpled 
foil,  in  which  is  inserted  the  brass  rod  carrying  the  ball,  and 
then  ascertaining  if  it  will  retain  a  charge  for  several  hours. 

337.  Exercise.  —  Support  a  Leyden  jar  on  a  pane  of  glass, 
and  try  to  charge  it  by  bringing  its  ball  in  contact  with  the 
prime  conductor  of  an  active  electrical  machine.  Compare  the 
intensity  of  the  charge  received,  with  that  received  in  the  same 
time  if  its  outer  surface  is  connected  with  the  other 
pole  of  the  machine.  Account  for  the  difference. 


338.  Exercise.  —  Fasten   about  a  Leyden  jar  a 
leather  or  cloth  belt  into  which  small  carpet-tacks  have 
been  driven,  with  the  points  extending  outward  from 
the  glass  (Fig.  131),  the  heads  being  in  contact  with 
the  foil.     Use  this  jar  as  in  the  last  experiment,  com- 
paring the  charge  received  when  insulated,  with  that  received  by 
the  same  jar  similarly  insulated,  but  without  the  belt.    Explain. 

339.  Exercise.  —  Charge  a  Leyden  jar  so  that  the  inner 
surface  is  positive,  and  a  second  one  so  that  the  inner  surface 
is  negative.     What  will  be  the  electrical  condition  of  the  outer 


MAGNETISM  AND  ELECTRICITY.  193 

surface  in  each  case?  Now  put  the  outer  surfaces  in  contact, 
and  see  if  they  discharge.  Suspend  a  pith-ball  midway  between 
the  balls,  and  account  for  it&  behavior. 

340.  Exercise.  —  Charge  a  Leyden  jar  having 
movable   metallic   coatings   (Fig.  132).      Separate 
the  jar  into  its  parts,  and  test  the  two  coatings  for 
electrification.      Put  the  parts  together,  and  then 
ascertain  if  there  is  any  charge.     What  appears  to 
be  the  office  of  the  coatings? 

In  taking  the  jar  apart,  the  inner  coating  should  not  come  in 
contact  with  the  hand. 

IX.    ELECTRICAL    MACHINES. 

341.  Apparatus.  —  Frictional    Machine,    Holtz    Machine, 
Electrophorus,  Proof-Plane,  Galvanometer,  Electroscope,  etc. 

342.  Exercise.  —  Make  the  following  tests  on  a  frictional 
plate-machine :  — 

1st,  Determine  the  kind  of  electrification  of  the  prime  con- 
ductor when  the  conductor  that  is  connected  with  the  rubbers  is 
joined  to  the  earth  by  a  chain.  In  like  manner,  test  the  combs. 

2d,  Determine  the  kind  of  electrification  of  the  rubbers 
when  the  prime  conductor  is  connected  with  the  earth. 

3d,  Examine  the  prime  conductor  for  manner  of  electrical 
distribution. 

4th,  Test  the  upper  and  also  the  lower  half  of  the  plate  for 
electrification. 

5th,  Separate  the  rubbers  from  the  earth,  and  ascertain  if  it 
affects  the  working  of  the  machine  as  shown  by  the  striking 
distance  of  the  spark. 


194  PRACTICAL   PHYSICS. 

6th,  Connect  the  rubbers  with  the  prime  conductor  by  means 
of  a  wire,  inserting  a  short-coil  galvanometer  in  the  circuit, 
and  determine,  by  the  indication*  of  the  galvanometer,  the 
direction  of  the  current.  See  Art.  347. 

343.  Exercise.  —  Charge  the  resinous  bed  of  an  Electro- 
phorus  (Fig.  133)  by  rubbing  it  with  a  piece  of  fur  or  flannel, 

and  determine  the  kind  of 
electrification .  Place  the 
metal  disk  in  contact  with 
the  bed,  touch  the  finger  to 
its  upper  surface  ;  then  re- 
move the  finger,  lift  the  disk 
by  its  insulated  handle,  and 
determine  its  electrical  condi- 
tion. Try  to  charge  the  disk 
Fl6  133  without  touching  it  with  the 

finger.     Account  for  the  dif- 
ference.    Explain  the  action  of  the  machine. 

To  make  an  electrophorus,  fill  a  pan  about  25  cm.  in  diameter 
and  2  cm.  deep  with  a  mixture  of  one  part,  by  weight,  of 
beeswax,  melted  with  five  parts  of  shellac.  For  a  cover,  cut 
out  of  sheet  zinc  a  disk  20  cm.  in  diameter ;  turn  over  the  edge 
neatly,  and  solder  it,  forming  a  rim  free  from  points  or  sharp 
edges.  Cement  to  its  centre  with  sealing-wax  a  piece  of  glass 
rod  for  a  handle. 

344.  Exercise.  —  Make   the   following   tests   on   a  Holtz 
machine  (Fig.  134)  :  — 

1st,    Determine  the  kind  of  electrification  of  each  armature. 
2d,    Determine  the  kind  of  electrification  of  different  parts 
of  the  stationar}7  plate. 


MAGNETISM  AND  ELECTRICITY.  195 

3d,    Test  the  combs. 

4th,    Test  the  surfaces  of  the  condensers. 

5th,  Connect  the  poles  of  the  machine  with  a  wire,  and 
insert  a  short-coil  galvanometer  to  determine  the  direction  of 
the  current.  See  Art.  347. 


FIG.  134. 


6th,  Connect  the  outer  surfaces  of  the  condensers,  inserting 
a  galvanometer  to  determine  the  direction  of  the  discharge ; 
i.e.,  to  determine  which  one  is  at  the  higher  potential. 

7th,  Compare  the  working  of  the  machine  when  the  con- 
densers are  attached,  with  that  when  removed. 

8th,  Determine  the  effect  on  the  spark  produced  by  exchan- 
ging the  balls  serving  as  poles,  for  others  of  larger  diameter. 


196  PRACTICAL   PHYSICS. 

9th,  Examine  in  a  dark  room  an  active  machine,  comparing 
the  appearance  of  positively  charged  points  with  those  which 
are  negative. 

10th,  Set  in  rapid  rotation,  by  means  of  a  whirling-machine, 
a  Newton's  color-disk  in  front  of  the  active  machine  in  a  dark 
room.  Watch  the  disk  during  each  discharge  to  ascertain  if  it 
is  seen  to  move  while  illuminated  by  the  spark.  What  inference 
can  you  make  regarding  the  duration  of  the  spark  ? 

11  th,  Compare  the  energy  expended  in  driving  the  machine 
when  excited,  with  that  when  not  excited.  Whence  the  elec- 
trical energy  ? 

X.    VOLTAIC    ELECTRICITY.  —  THE    BATTERY. 

345.  Apparatus.  —  Zinc,  Copper,  Iron,  Lead,  etc. ,  in  Sheet 
Form  ,  Tumbler,  Compass,  Insulated  Wire,  etc. 

346.  Exercise.  —  Cut  from  sheet  zinc  a  strip  about  10  cm. 
long  and  3  cm.  wide,  and  from  sheet  copper  a  second  one  of 
the  same  size.      Fasten  to  one  end  of  each  of  these  a  piece 
of  No.  20  copper  wire  about  20  cm.  long,  either  by  soldering, 
or  by  passing  the  end  of  the  wire  through  a  small  hole  punched 
in  the  strip,  and  twisted  on  itself  so  as  to  make  a  good  contact. 
Fill  a  common   tumbler  about  two-thirds   full  of  water,   and 
add  to  it  slowly  about  one-twentieth  as  much  sulphuric  acid 
(commercial).     Now  hold  the  zinc  strip  vertically  in  this  dilute 
acid  for  a  few  minutes,  observe  closely  the  surface  of  the  zinc, 
and  record  any  changes.     Then  place  the  copper  strip  in  the 
tumbler,    holding    it    near   the    zinc,    parallel    to    it,    but   not 
touching  it,  and  ascertain  whether  its  presence  in  any  way 
affects    the   previously    noted   phenomenon.      Now    touch   the 
outer  ends  of  the  two  strips,  or  the  two  attached  wires,  and 


MAGNETISM  AND   ELECTRICITY.  197 

note  the  effect,  if  any.     Go  over  these  steps  several  times  to 
make  sure  that  what  was  seen  was  no  accidental  occurrence. 

Wash  the  zinc  strip  thoroughly  in  water,  rubbing  it  with  a 
cloth  to  remove  the  black  particles  of  carbon  from  its  surface. 
It  may  be  found  necessary  to  scour  the  zinc  with  sand.  Apply 
with  a  cloth  kept  for  the  purpose  a  little  mercury,  performing 
the  operation  on  a  common  earthen  plate.  But  little  pressure 
should  be  used  in  applying  the  mercury,  to  avoid  breaking  the 
zinc.  Remove  all  jewellery  from  the  hands  before  handling 
mercury.  Replace  the  zinc  in  the  dilute  acid,  and  repeat  all 
the  tests  which  were  made  with  the  unamalgamated  zinc,  com- 
paring each  observation  with  the  corresponding  one  previously 
made. 

Ascertain  the  effect  on  the  phenomena  attending  the  strips, 
when  in  the  acid,  of  connecting  the  two  wires  with  a  short  strip 
of  cotton,  instead  of  touching  their  ends.  Try  successively  a 
piece  of  silk,  wood,  paper,  gilt-paper,  glass, 
tin-foil,  silver,  wax,  etc. 

If  mercury  should  get  on  the  copper  strip, 
remove  it  by  heating  the  strip  in  a  flame.  In- 
stead of.  joining  the  ends  of  the  wires  together 

FIG. 135. 

by  twisting   them,   it  is  preferable  to  employ 

Connectors   (Fig.  135).      The   connection   could   be   made  by 

dipping  the  ends  into  a  small  cup  of  mercury. 

347.  Exercise.  —  Prepare  strips  of  zinc  and  of  copper  as 
in  the  last  experiment.  Clean  the  zinc  thoroughly  in  dilute 
sulphuric  acid,  and  amalgamate  it  by  rubbing  it  with  mercury. 
Tack  these  strips  on  opposite  sides  of  a  piece  of  wood  one 
centimetre  wide  and  about  12  cm.  long,  being  careful  that  the 
tacks  from  opposite  sides  do  not  touch.  Place  these  strips  in 
a  tumbler  two-thirds  full  of  dilute  sulphuric  acid.  Connect  the 


198 


PRACTICAL   PHYSICS. 


free  ends  of  the  wires,  and  then  stretch  a  portion  of  the  wire 
over  a  compass-needle,  or  a  magnetic  needle  mounted  as  hi 

Fig.  136,  holding  it  parallel 
to  it.  Record  the  effect 
produced  on  the  needle. 
Compare  the  effect  with  that 
produced  by  placing  the  wire 
below  the  needle.  Reverse 
the  wire  without  changing 
the  position  of  the  plates, 
and  compare  the  effect  with 
that  previously  obtained. 


FIG.  136. 


FIG. 137. 


Assuming  that  there  is  an   electric  current 

flowing  through  the  wire  from  the  copper  to 

the  zinc,  express   as  a  law  the  behavior  of 

the  needle  on  passing  the  current  parallel  to 

it.      See  if  it  is  possible  to  hold  the  right 

hand  so  that  the  index  finger  will  point  out 

the  direction  of  the  current,  while,  at  the 

same  time,  the  thumb  will  point  out  the  di- 
rection of  the  needle  deflection. 
Fig.  137  shows  a  form  of  ap- 
paratus known  as  Oersted's  Par- 
allelogram, that  is  well  adapted 
to  the  work  just  described. 

Ascertain  the  effect  on  the 
needle  of  passing  the  current 
entirely  around  it  (Fig.  138)  by 
bending  the  conducting  wire  into 

a  rectangular  form,  and  placing  the  needle  within  it.     Try  two 

turns  of  wire  about  the  needle.     Try  several.     Inference. 
A  simple   method   of   placing  a  magnetic   needle   within  a 


FIG.  138. 


MAGNETISM  AND  ELECTRICITY.  199 

looped  conductor,  as  required  above,  is  to  set  a  common 
pocket-compass  in  a  hole  cut  in  a  square  piece  of  board  15  mm. 
thick,  and  a  little  longer  on  the  edge  than  the  diameter  of  the 
compass.  Around  this  board,  wind  insulated  copper  wire 
(No.  20),  as  many  layers  as  needed.  The  ends  of  the  wire  can 
be  fastened  by  driving  short  brass  wire  staples  into  the  block. 
This  will  be  found  a  very  serviceable  galvanometer  for  many 
of  the  experiments  that  follow.  Binding-posts  screwed  into 
the  block  will  make  it  easier  to  place  it  in  a  battery-circuit. 
Double  connectors  may  be  used  instead. 

To  facilitate  reversing  the  current,  as  required  above,  a 
device  called  a  Commutator  may  be  used.  One  may  be  made 
as  follows  :  — 

Bore  two  holes  one  centimetre  deep,  and  one  centimetre  apart, 
in  a  block  of  wood.  In  these  pour  mercury,  connecting  each  to 
a  binding- post  screwed  into  the  block  by  a  short  heavy  copper 
wire.  The  galvanometer  is  to  be  connected  tc  the  binding-posts, 
the  battery  to  the  mercury-cups.  To  reverse  the  current,  it  will 
be  necessary  simply  to  cross  the  battery-wires. 

Test  the  rule  for  determining  the  direction  of  a  battery-current 
by  means  of  a  galvanometer,  by  having  some  one  connect  it  to 
a  batteiy-cell  so  placed  that  you  do  not  see  the  order  of  connec- 
tion made  ;  then,  by  observing  the  direction  of  deflection  of  the 
needle,  determine  which  wire  is  joined  to  the  zinc  plate. 

348.  Exercise.  —  Make  a  voltaic  element  out  of  strips  of 
zinc  and  sheet-iron  after  the  plan  given  in  the  last  experiment. 
Place  the  plates  in  dilute  sulphuric  acid,  connect  the  poles  to 
the  galvanometer,  and  determine  which  is  the  positive  one. 
Try  iron  and  copper ;  lead  and  copper ;  zinc  and  lead  ;  iron 
and  lead. 


200  PRACTICAL   PHYSICS. 

XI.    EFFECTS    OF    ELECTRICAL    CURRENTS. 

349.  Apparatus.  —  Battery,  File,  Galvanometer,  Apparatus 
for  Electrolysis,  Fine  Wire,  etc. 

350.  Exercise.  —  Twist  the  wire  leading  from  one  of  the 
poles  of  a  batter}^  about  one  end  of  a  file,  and  the  other  wire 
about  a  steel  nail.     Now  draw  the  nail  across  the  rough  file 
surface.     Note  the  attending  phenomenon.     Apply  the  finger 
to  the  end  of  the  nail  after  drawing  it  several  times  over  the 
surface  of  the  file,  and  ascertain  if  there  has  been  any  change 
in  its  temperature.     Inference. 

351.  Exercise.  —  Fasten  to  each  pole  of  some  convenient 
form  of  battery  a  short  piece  of  No.  18  copper  wire.     Using 
connectors,  join  their  ends  with  a  piece  of  No.  30  platinum 
wire  3  cm.  long.     Close  the  circuit,  and  observe  the  effect  on 
the   platinum  wire.      Try   fine    iron   wire.      Try   copper  wire. 
Ascertain  if   the  size  or  the  length  of  the  wire  makes   any 
difference.       Are    wires    of    different    metals    affected    alike  ? 
Place  the  galvanometer  of  Art.  347  in  circuit  with  the  battery, 
and  take  the  reading.     Now  insert  the  short  piece  of  fine  wire 
in  the  same  circuit,  and  again  read  the  galvanometer.     What 
is  indicated  by  the  decrease  in  the  deflection  of  the  needle? 
What  have  you  as  an  equivalent  for  the  loss  of  electric  current  ? 

The  battery  used  must  give  a  strong  current.  The  chromic 
acid  battery  is  recommended.  Any  short- coil  galvanometer 
can  be  used.  Be  careful  to  place  it  so  that  the  wire  of  the  coil 
is  parallel  to  the  needle  before  closing  the  circuit. 

352.  Exercise.  —  Make  a  paper  tube  5  cm.  long  and  1  cm. 
in  diameter.     Fit  corks  to  the  ends.     Through  one  of  them. 


MAGNETISM   AND    ELECTRICITY. 


201 


FIG.  139. 


put  two  pieces  of  No.  18  copper  wire,  joining  their  inner  ends 
with  a  short  piece  of  No.  30  iron  wire.  Fill  the  tube  with  gun- 
powder, close  the  ends  with  corks,  and  connect  the  terminals 
with  long  wires  to  the  poles  of  a  battery  of  two  or  three 
chromic  acid  cells  located  at  some  distance  from  the  torpedo. 
Now  close  the  circuit.  Explain. 

Try  a  torpedo  having  the  ends  of 
the  copper  wires  not  joined  by  a  fine 
wire,  but  bent  together,  leaving  a 
break  of  about  2  mm.  Connect  the 
terminals  to  the  surfaces  of  a  heavily 
charged  Leyden  jar.  Explain.  The 
Electrical  Mortar  (Fig.  139),  or  the 
Gas-Pistol,  may  be  used  in  place  of 

the  torpedo  to  illustrate  the  heating  effects  of  the  electric 
spark. 

353.     Exercise.  —  Bend   a   glass   tube    of   about    1.5   cm. 
diameter  and   15  cm.  long  into  a  V-form.     Close  the  ends  with 

corks  and  thrust  through  them 
platinum  wires  (Fig..  140),  ter- 
minating within  the  tube  in  strips 
of  platinum  foil  2  mm.  wide  and 
3  cm.  long,  and  reaching  within  5 
cm.  of  each  other.  The  foil  should 
be  soldered  to  the  wires,  and  var- 
nished at  the  junction  to  prevent 
chemical  action  on  the  solder.  The  tube  may  be  supported  in 
a  burette-holder,  or  by  setting  it  into  a  slot  cut  into  the  side  of 
an  empty  chalk-box.  Fill  this  V-tube  two-thirds  full  of  a 
solution  of  sodium  sulphate,  colored  with  litmus  or  the  liquor 
obtained  by  boiling  purple  cabbage  in  water.  Connect  the 


140. 


202 


PRACTICAL    PHYSICS. 


terminals  to  the  poles  of  a  battery  of  two  or  three  cells  joined 
in  series  (Art.  369).  Remembering  that  the  action  of  an  acid 
on  a  vegetable  purple  is  to  turn  it  red,  and  that  of  an  alkali 
is  to  give  it  a  greenish  tinge,  what  effect  do  you  find  the 
electric  current  has  on  the  solution  of  sodium  sulphate  ?  Try 
copper  sulphate.  Try  tin  chloride.  Use  quite  dilute  solu- 
tions, and  omit  the  coloring  matter  in  the  last  two  cases. 

354.     Exercise.  —  Cut   the  bottom   from  a  wide-mouthed 

bottle  having  a  diameter  of  about  8  cm.  Insert  a  good  cork  in 
the  neck,  and  through  it  thrust  two  platinum 
wires  terminating  within  the  bottle  in  strips  of 
platinum  foil  set  parallel  to 
each  other,  and  one  centi- 
metre apart.  Fill  the  bottle 
two-thirds  full  of  slightly  acid- 
ulated water,  and  support  it 
on  the  ring  of  the  iron  stand. 
Over  these  electrodes,  invert 
long  test-tubes  also  filled  with 
the  acidulated  water.  Now 
place  the  apparatus  (Fig.  141) 

in  circuit  with  a  battery  of  two  or  three  cells 

connected  in  series  (Art.  369).     Ascertain  the 

relative  amount  of  gases  liberated  during  any 

interval  of  time  by  measuring  the  length  of 

the  column.     Remove  each  test-tube  by  hold- 
ing the  finger  firmly  over  its  mouth ;    invert, 

and  apply  a  lighted  match.     The  one  that  burns  with  a  slight 

explosion  is  hydrogen  ;  the  other  is  oxygen. 

Reverse  the  current  through  the  apparatus,  and  ascertain  if 

there  is  any  difference  in  the  liberation  of  the  gases. 


FIG. 141. 


FIG. 142. 


MAGNETISM    AND    ELECTRICITY. 


203 


Ascertain  the  effect  of  increasing  the  number  of  cells  in 
the  battery.  Compare  two  different  batteries  by  observing  the 
length  of  the  hydrogen  column  produced  by  each  during  the  same 
interval  of  time.  A  convenient  form  of  apparatus  for  effecting 
the  decomposition  of  liquids  by  means  of  the  electric  current  is 
shown  in  Fig.  142.  The  gas  can  be  drawn  off  by  means  of  a 
rubber  tube,  and  tested.  This  tube  must  be  filled  with  water  to 
expel  the  air.  Why?  The  measurement  is  readily  effected  by 
having  the  tubes  graduated. 

355.  Exercise.  —  Dampen  a  sheet  of  printing- paper  with  a 
solution  of  ferrocyanide  of  potassium  and  ammonium  nitrate. 
Lay  it  on  a  brass  plate  connected  with  the  negative  pole  of  the 
battery.     Connect  the  positive  pole  of  the  battery  with  a  piece 
of  iron  or  steel  wire.     Use  this  wire  as  a  pencil,  and  write  on 
the  prepared  paper.     Compare   the  effect  with  that  produced 
when  trying   to    write  with   the    wire    not   in   the 

battery  circuit.     Explain. 

356.  Exercise.  —  Wind   neatly   on  a  rod   of 
annealed  iron  about  10  cm.  long  and  1  cm.  or  less 
in  diameter,  two  or  three  layers  of  insulated  copper 
wire   No.  18  or  20   (Fig.   143).      Put  the  wire  in 

circuit  with  a  bat- 
tery, and  examine 
the  iron  core  for 
magnetic  proper- 
ties. Break  the 

circuit,  and  again  test  the  rod.     Jar  the  rod  a  little,  and  again 

test  it. 

Support  the  apparatus  on  a  sounding-board   (Fig.  144),  and 

listen  intently  near   the  coil    as    the  battery  circuit  is  opened 


FIG. 144. 


FIG.  143. 


204  PRACTICAL    PHYSICS. 

and  closed.  What  is  the  probable  origin  of  the  phenomenon? 
What  is  suggested  by  this  experiment  regarding  the  nature 
of  magnetism? 

XII.      ELECTRICAL    MEASUREMENTS. 

a.    Resistance  of  Conductors. 

357.  Apparatus.  —  Galvanometers,  Daniell's  Battery,  Set 
of  Resistance  Coils,  Wheatstone's  Bridge,  Insulated  Wires,  etc. 

358.  Exercise.  —  Measure  the  resistance  in  ohms,  of  an 
electrical  conductor. 

There  will  be  needed  for  this  work  a  Constant  Battery,  a 
Galvanometer,  and  a  set  of  Resistance  Coils.  For  most 
purposes,  the  Daniell's  battery  will  be  found  sufficiently 
constant.  Of  galvanometers  there  are  a  great  many  forms, 
each  possessing  its  special  points  of  excellence.  In  selecting 
one  for  any  line  of  work,  regard  must  be  had  for  the  condi- 
tions under  which  it  is  to  be  used.  If  the  current  is  feeble, 
owing  to  the  great  resistance  of  the  circuit,  a  long-coil  gal- 
vanometer should  be  chosen  in  order  that  a  suitable  deflec- 
tion of  the  needle  may  be  obtained.  A  galvanometer  having 
two  or  more  coils  is  to  be  preferred  for  general  use,  as 
then  the  resistance  can  be  adapted  to  the  case.  A  deflec- 
tion of  the  needle  of  between  25  degrees  and  55  degrees  is 
preferable. 

A  serviceable  tangent  galvanometer  is  easily  made  as  fol- 
lows :  Cut  out  of  well-seasoned  wood  a  ring  30  cm,  in  diame- 
ter, and  having  a  cross-section  of  2.5  cm.  square.  Mount  this 
on  a  circular  wooden  base  provided  with  levelling-screws 
(Fig.  145).  No  iron  must  enter  into  the  construction.  In  the 


MAGNETISM   AND    ELECTRICITY. 


205 


outer  edge  of  the  ring,  cut  a  rectangular  groove  2  cm.  wide  and 
2  cm.  deep.  In  this  groove  wind  two  turns  of  heavy  copper 
wire,  the  ends  to  be  connected  to  binding-posts  on  the  base. 
This  will  give  a  coil  of  practically  no  resistance.  Now  wind  in 
the  same  groove,  using  insulated 
copper  wire  No.  26,  three  other 
coils  of  10,  30,  and  90  turns 
respectively,  the  ends  of  each  to 
be  connected  to  its  own  pair  of 
posts.  By  making  connections, 
so  as  to  secure  the  sum  or  differ- 
ence of  these  coils,  any  of  the 
following  series  can  be  secured  : 
10,  20,  30,  etc.,  130  turns.  Fas- 
ten across  the  ring  a  wooden  or 
brass  bar  supporting  a  wooden 
or  paper  box  10  cm.  in  diameter 
and  5  cm.  deep,  having  a  glass  cover  with  a  hole  1  mm.  in 
diameter  drilled  through  its  centre.  Place  on  the  bottom  of 
this  box  a  circular  piece  of  mirror-glass  to  which  is  cemented  a 
paper  ring  graduated  to  degrees.  For  a 
needle,  magnetize  a  piece  of  watch-spring 
15  mm.  long,  inserting  it  edgewise  into  a 
disk  of  elder-pith  (Fig.  146).  Cement  to 
the  pith-disk,  at  right  angles  to  the  needle, 
a  pointer  of  glass  thread  made  by  drawing 
out  a  piece  of  glass  tubing  when  thoroughly 
softened  in  a  flame.  Suspend  the  needle 
by  a  silk  fibre  from  the  centre  of  the  glass  cover.  The  needle 
should  hang  at  the  centre  of  the  wooden  ring,  and  within  a 
few  millimetres  of  the  scale.  When  the  instrument  is  levelled, 
the  two  ends  of  the  pointer  should  give  the  same  readings, 


FIG.  145. 


FIG. 146. 


206 


PRACTICAL  PHYSICS: 


and  reversing  the  current  should  not  alter  the  amount  of  the 
deflection ;  if  it  does,  the  pointer  is  either  not  set  at  right 
angles  to  the  needle,  or  the  needle  is  not  properly  centred.  To 
eliminate  small  errors  of  this  kind,  average  the  readings  of 
both  ends  of  the  pointer ;  reverse  the  current,  and  average  the 
readings  ;  and  finally  average  these  two  averages  for  the  correct 
reading. 

In  Fig.  147  is  shown  a  more  sensitive  form  of  galvanometer, 
where  a  form  of  needle  known  as  Astatic  is  employed.     Such 
an  instrument  is  desirable  for  use  in  con- 
nection  with   Wheats  tone's    bridge  or  the 
thermopile. 

For  most  of  the  work  in  this  book,  a 
galvanometer  constructed  as  follows  will 
be  sufficiently  reliable  :  Procure  a  circular 
wooden  box  10  cm.  in  diameter  and  10  cm. 
deep,  having  a  wooden  cover  with  a  large' 
circular  hole  cut  in  it,  exposing  the  bottom 
clearly  to  view.  On  the  bottom,  place  a 
wooden  block  2  cm.  thick,  on  which  is 
wound  a  flat  coil  of  several  layers  of  No.  24  insulated 
copper  wire.  Bring  the  ends  through  the  side  of  the  box, 
and  fasten  them  to  small  binding-posts.  The  scale  and  the 
needle  are  prepared  as  in  the  case  of  the  tangent  galvanometer 
described  above.  To  the  under  side  of  the  ring-cover,  cement 
a  clean  plate  of  glass.  Attach  the  fibre  supporting  the  needle 
to  the  centre  of  the  cover.  This  must  be  done  with  great  care, 
for,  if  not  centred,  the  two  ends  of  the  pointer  will  give 
different  readings  as  the  cover  is  turned  around.  This  instru- 
ment may  be  used  as  a  tangent  galvanometer,  owing  to  its 
short  needle,  without  sensible  error,  for  angles  not  exceeding 
45  degrees. 


FIG. 14< 


MAGNETISM    AND    ELECTRICITY. 


207 


FIG.  148. 


If  the  coil  is  wound  in  two  parts,  as  shown  in  Fig.  148,  the 
distance  between  the  parts  being  a  trifle  less  than  the  length  of 
the  needle,  it  has  been  found  that  the 
deflection  is  proportional  to  the  cur- 
rent  up   to    50    degrees.     When  no 
current  is  passing  through  the  coils, 
the  needle  should  hang  symmetrically 
between  them. 

Resistance-boxes  usually  consist  of 
a  collection  of  coils  of  insulated  Ger- 
man-silver wire  of  dif- 
ferent lengths  and  de- 
grees of  fineness,  and 
consequently  of  differ- 
ent resistances,  -each 
coil  having  some  known 
relation  to  the  standard 
unit  of  resistance,  the 
Ohm.  By  means  of 

movable  arms  or  plugs,  as  the  case  may  be,  any  required  resist- 
ance can  be  thrown 
into  the  circuit  (Fig. 
149):  Fig.  150  shows 
a  cheap  form  of  re- 
sistance-box suitable 
for  beginners.  To 
close  the  circuit,  each 
switch  must  rest  on  a 
brass  nail-head  of  the 
corresponding  gradu- 
ated arc.  These  contacts  must  be  kept  bright  to  insure 
good  work.  In  using  coils,  do  not  keep  the  circuit  closed 


FIG.  149. 


208  PRACTICAL    PHYSICS. 

for  any  great  length  of  time,  as  they  become  heated  from  the 
current. 

First  Method.  —  Form  a  circuit  consisting  of  a  constant 
battery  B,  a  galvanometer  G,  a  set  of  resistance  coils  R, 
and  the  conductor  X  to  be  measured  (Fig.  151).  By  discon- 
necting X,  and  inserting  the  short  thick  wire  W,  the  coil 
may  be  cut  out  of  the  circuit.  First, 
take  the  reading  of  G  when  sufficient 
resistance  has  been  introduced  by  means 
of  R  to  produce  a  suitable  deflection. 
r_J  /^T^  Secondly,  insert  W,  dropping  X  out  of 

-,  V./       the  circuit,  and  add  sufficient  resistance 

through  R.  to  produce  the  same  reading 
for  G.  The  added  resistance  is  evidently 
equal  to  that  of  X.  The  deflection  of 


the  galvanometer  had  better  not  exceed 
Fi^  151  45  degrees.    The  accuracy  of  this  method 

is  dependent  very  largely  on  the  sensi- 
tiveness of  the  galvanometer,  and  the  constancy  of  the  battery. 
It  is  more  accurate  for  small  resistances  than  it  is  for  large 
ones.  Be  as  expeditious  as  possible  in  making  the  required 
observations,  that  the  conditions  may  change  as  little  as 
possible.  It  is  recommended  to  place  a  telegraph  key  in  the 
circuit  to  make  and  break  connections. 

Second  Method.  —  Form  a  circuit  consisting  of  a  constant 
battery  B,  a  tangent  galvanometer  G,  a  set  of  resistance  coils 
R,  and  the  conductor  X  to  be  measured,  using  as  little  wire  as 
possible  in  making  the  connections.  Represent  the  resistance 
of  the  battery  by  r,  which,  if  unknown,  can  be  determined  by 
Art.  367,  and  that  of  the  galvanometer  by  g,  which,  if  unknown, 
can  be  determined  by  the  first  method  of  measuring  resistances 
of  conductors,  employing  a  second  galvanometer  as  a  galvano- 


MAGNETISM    AND    ELECTRICITY. 


209 


scope,  or  as  in  Art.  365.  Adjust  G  and  R  so  as  to  secure  a  de- 
flection between  25  degrees  and  55  degrees.  With  a  resistance 
R  and  the  unknown  X  in  the  circuit,  take  the  reading  of  G  which 
may  be  represented  by  a.  Now  cut  out  X,  and  introduce 
a  resistance  R'  by  means  of  the  resistance-box,  to  give  a 
different  deflection  of  G,  as  a'.  Substitute  the  values  obtained 

tan  a' 


in  the  formula 


Proof. — By  Ohm's  law,  C  =  -. 


tana 
E 


,  and  solve  for  X. 


,  and  O' =—-?-—. 
R'+r+g 


By   the   law  of    the    Galvanometer,  /^  = 


tan  a' 


Therefore 


_^_  r  _|_  y  _[_  X  __  tan  a' 
R '  -f-  r  +  g       "  tan  a  * 


As  the  resistance  of  a  battery  varies  somewhat  with  the 
external  resistance,  it  is  advisable  to  employ  one  having  as  low 
a  resistance  as  possible,  and,  at  the  same  time,  make  the 
external  resistance  large  in  comparison,  so  that  the  effect  on 
the  constancy  of  the  battery  of  changing  the  external  resist- 
ance may  be  small.  The  best  results  are  obtained  by  securing 
a  deflection  as  near  as  pos- 
sible  to  45  degrees,  and  hav- 
ing a  and  a'  nearly  equal. 
When  the  external  resistance 
is  large  in  comparison  with 
the  battery  resistance,  the 
latter  may  be  neglected  with 
but  slight  error. 

Third  Method.  —  For  this 
method  is  needed  a  Wheat-  FlG>  152' 

stone's    bridge    and  an   astatic   galvanometer.     The   principle 
applied  is,  that,  if  a  circuit  be  set  up  as  shown  in  Fig.  152, 


210 


PRACTICAL    PHYSICS. 


and  R,  R',  and  R"  so  adjusted,  that,  on  closing  the  circuit, 
no  deflection  of  G  is  produced,  then  R'X  =  RR" ,  whence 

RR" 
X  =  —nT'     Fig.  153  illustrates  a  simple  form  of  the  Bridge, 

in  which  two  of  the  resistance-boxes  are  replaced  by  a  fine 
German-silver  wire.  This  is  constructed  as  follows :  On  a 
varnished  board  1.1  metre  long  and  15  cm.  wide,  fasten  with 
brass  screws  strips  of  copper  or  brass  1.5  cm.  wide,  of  the  form 
shown  in  the  figure,  the  pieces  ME  and  HF  being  10  cm. 
long.  The  spaces  between  A  and  the  cross-pieces  may  be  one 

centimetre.    The 
~^  lengths    of     the 

strips  should  be 
such  that  the  in- 
side distance  be- 
tween E  and  F 
is  exactly  one 
metre.  Solder  a 
stretched  Ger- 
man-silver wire  (No.  26)  across  from  E  to  F.  Under  this 
wire  fasten  a  paper  scale  divided  to  half -centimetres.  Solder 
binding-posts  to  these  strips  so  that  connections  may  be  made 
as  shown  in  the  figure,  the  contact  at  B  being  made  by  pressing 
the  wire  from  the  galvanometer  against  the  wire  of  the  bridge. 
In  making  connections,  use  coarse  wire,  and  as  little  as  possi. 
ble,  that  the  resistance  of  these  wires  may  be  neglected. 

To  use  the  bridge,  make  the  connections  as  already  indicated  ; 
through  R,  introduce  1,  10,  or  100  ohms;  then  slide  B  along 
the  wire  EF  till  a  point  is  reached  at  which  the  reading  of  G 
is  zero ;  then  X  equals  the  reading  of  R  multiplied  by  the 
ratio  of  EB  to  BF. 

This  method  is  unaffected  by  any  changes  in  the  electrical 


TZI 


FIG.  153. 


MAGNETISM   AND    ELECTRICITY.  211 

current,  the    degree    of    accuracy    secured    depending   on   the 
sensitiveness  of  the  galvanometer. 

359.  Exercise.  —  Measure  the  resistance  of  40  metres  of 
insulated  copper  wire,  and  also  of  20  metres  of  the  same  kind 
of  wire.     Compare  the  resistance  with  the  lengths.     Inference. 

360.  Exercise.  —  Measure  the  resistance  of  40  metres  of 
insulated  copper  wire  (No.  23),  and  also  of  the  same  length 
of  No.  30  wire.     Compare  the  resistances  with  the  diameters. 
Inference. 

361.  Exercise.  —  Compare  the  resistances  of  equal  lengths 
of   wires  of   different   substances   having   the  same   diameter. 
Inference. 

362.  Exercise.  —  Compare   the  resistances  of    two  equal 
wires  of  the  same  material  laid  side  by  side,  and  connected  at 
their  ends,  witli  that  of  one  of  them  taken  separately. 

363.  Exercise. —  Measure  the  resistance  of  a  coil  of  fine 
wire  of   known  diameter,  but  whose  length  is  unknown,  and 
also  measure  the  resistance  of  a  Jcnoiun  length  of  wire  of  the 
same   kind.     Calculate   the    length  of    the    unknown   coil   by 

the  formula  —  =  -,  R  and  I  representing  resistance  and  length 
respectively. 

364.  Exercise.  —  Determine  the  effect  of  change  of  tem- 
perature on  electrical  conductivity. 

In  Wheatstoiie's  bridge,  for  X  put  one  metre  of  fine  wire 
(No.  30)  made  into  a  coil  by  winding  it  carefully  on  a  pencil, 
not  allowing  the  successive  parts  of  the  coil  to  touch,  so  that 


212  PRACTICAL    PHYSICS. 

the  current  must  pass  through  its  entire  length.  Now  set  B 
so  as  to  produce  a  balance  ;  then  hold  a  Bunsen  flame  under 
the  coil ;  notice  the  effect  on  the  balance,  and  ascertain 
whether  the  conductivity  is  increased  or  diminished  by  moving 
B  till  the  balance  is  restored. 

Compare  iron,  copper,  and  German-silver  wires  in  this  way 
to  see  if  they  are  equally  affected. 

The  general  effect  that  the  lowering  of  the  temperature  of  a 
conductor  has  upon  its  conductivity  may  be  roughly  shown  by 
connecting  the  poles  of  a  strong  battery  with  a  short  piece  of 
iron  wire  of  such  a  length  that  the  current  heats  it  to  a  dull  red 
color.  Now  apply  a  lump  of  ice  to  one  portion  of  the  wire, 
and  observe  the  effect  on  the  other  part.  Inference. 

365.  Exercise.  —  Measure  the  resistance  of  a  galvanometer 
by  means  of  its  own  deflection. 

First  Method.  —  Connect,  in  circuit,  the  galvanometer,  a 
constant  battery  of  known  resistance,  and  a  set  of  resistance 
coils,  employing  short  thick  wire.  Proceed  as  in  Art.  358 
(second  method),  except  that  the  X  is  omitted.  By  giving,  in 
succession,  two  values  to  72,  as  K  and  J?',  two  values  for  a 
are  obtained,  as  a  and  a'.  Now  substitute  in  the  formula 

R  4-  r  4-  a      tan  a 

-  —  —    — 5  and  solve  tor  q.     It  will  be  necessary  to 

^  +  r  H~  9      tan  a 

determine  the  battery  resistance  unless  it  is  known  to  be  small 

in  comparison  with  R  and  g. 

Second  Method.  —  Place  the  galvanometer  in  the  place  of  X 
in  Whcatstone's  bridge,  joining  the  posts  A  and  B  (Fig.  153), 
previously  connected  by  the  galvanometer,  by  a  short,  thick 
wire.  A  deflection  of  Q  is  now  obtained.  Now  place  a  bar 
magnet  in  the  magnetic  meridian,  so  that,  by  its  attraction, 
the  deflection  of  the  needle  is  reduced  to  zero.  Adjust  the 


MAGNETISM  AND  ELECTRICITY.  213 

resistance  in  the  arms  of  the  bridge,  so  that  the  reading  of  G-  is 
not  changed  by  connecting  or  disconnecting  A  and  B.  Then 

RR" 

R  g  —  KH"  whence  g  =         . 

b.    Resistance  of  Batteries. 

366.  Apparatus. —  Darnell's    Battery,    Galvanometer,    Re- 
sistance Coils,  Wheatstone's  Bridge,  etc. 

367.  Exercise.  —  Measure  the  internal   resistance   of    a 
battery. 

First  Method.  —  Place  the  cell  whose  resistance  is  required 
in  circuit  with  a  tangent  galvanometer  of  known  resistance 
y,  and  a  set  of  resistance  coils.  Introduce  through  the  coils 
a  resistance  of  R  and  observe  the  deflection  a  of  G.  Then 
introduce  a  different  resistance  R',  and  observe  the  deflection 

a'  of  G.     Substitute  in  the  formula  R    '   g  ~^~ r  = tan  a',  and 

R' -\-g-\-r      tana 

solve  for  r.  Do  not  use  too  large  deflections  of  the  galvanom- 
eter, as  beyond  45°  the  needle  moves  out  of  a  uniform  field. 

Second  Method.  —  When  two  cells  of  the  same  kind  are 
available,  then  connect  them  in  opposition,  that  is,  with  a 
short  thick  wire  join  the  two  negative  poles ;  and  then,  by 
means  of  their  positive  poles,  place  them  in  circuit  with  a  con- 
stant battery,  a  galvanometer,  and  a  set  of  resistance  coils. 
Since  two  equal  cells,  joined  in  opposition,  neutralize  each 
other,  then  any  deflection  of  the  galvanometer  must  be  due  to 
the  constant  battery.  Hence,  two  such  cells  can  be  treated  as 
a  dead  conductor,  and  the  resistance  measured  as  in  Art.  358. 
Half  of  this  resistance  is  that  of  one  of  the  cells. 

It  will  be  found,  however,  on  connecting  two  cells  in  opposi- 
tion and  placing  them  in  circuit  with  a  galvanometer,  that  a 


214  PRACTICAL  PHYSICS. 

feeble  current  is  furnished,  showing  that  the  cells  are  not  quite 
equal.     Hence  this  method  is  not  very  reliable. 

Third  Method.  —  Place  the  battery  in  the  place  of  X  in 
Wheatstone's  bridge  (Fig.  153),  connecting  C  and  D  by  a  wire. 
Now  set  R  as  nearly  equal  to  the  resistance  of  the  battery  as 
can  be  estimated,  and  find  a  position  for  B,  such  that  G-  main- 
tains a  constant  deflection  whether  the  circuit  is  closed  between 

7~>  ~f>  ll 

C  and  D  or  not.     Then  r  =         — .     It  is  better  to  employ  a 

controlling  magnet,  and  bring  the  galvanometer  reading  down 
to  zero,  as  then  the  instrument  is  most  sensitive. 

The  accurate  measurement  of  the  resistance  of  a  battery  is 
not  easy,  as  it  varies  with  the  resistance  in  the  circuit  at  the 
time,  and  is  constantly  changing  with  the  chemical  changes 
going  on  in  the  cell.  The  most  that  should  be  expected  is  to 
get  an  approximation  to  its  resistance,  under  the  conditions 
governing  the  battery  during  the  time  it  was  under  examination. 
Employing  high  resistances  would  tend  to  retard  polarization  ; 
but  their  use  would  be  open  to  the  objection  that  errors  in  such 
high  resistances  will  introduce  errors  into  the  results  obtained 
larger  than  the  battery  resistance.  Unless  you  have  the  most 
accurately  constructed  apparatus  it  is  better  to  employ  resist- 
ances but  little,  if  any,  greater  than  those  being  measured  ;  and, 
in  case  the  galvanometer  is  over-sensitive  and  gives  too  large 
a  deflection,  reduce  its  deflection  by  a  controlling  magnet,  or 
employ  a  shunt,  of  known  value,  and  compute  the  resistance 
of  the  shunted  instrument,  as  shown  in  Art.  376. 

368.  Exercise.  —  Determine  whether  the  size  of  the  plates 
and  the  distance  between  them  affect  the  resistance. 

Construct  a  simple  cell,  as  in  Art.  346.  Measure  the  in- 
ternal resistance,  when  the  plates  reach  8  cm.  into  the  exciting 


MAGNETISM  AND  ELECTRICITY.  215 

fluid,  and  compare  with  that  when  they  reach  only  4  cm.  into  the 
liquid.  Also  measure  the  resistance  when  the  plates  are  3  cm. 
apart,  and  compare  with  that  when  1.5  cm.  apart.  Inference. 

Polarization  may  be  prevented  during  the  experiment  by 
keeping  up  a  gentle  agitation  of  the  liquid,  by  means  of  a 
small  glass  rod. 

369.  Exercise.  —  Compare  the  resistance  of  two  cells,  of 
the  same  size  and  kind  when  joined  abreast,  with  that  of    a 
single  cell.    Also  measure  their  resistance  when  joined  in  series. 
Inferences. 

To  connect  cells  abreast,  join  their  like  poles  together, 
making  of  them  one  pole.  To  connect  them  in  series,  join  th.e 
positive  pole  of  one  to  the  negative  pole  of  the  next,  thus 
leaving  the  negative  pole  of  the  first  cell  and  the  positive  pole 
of  the  last  one  to  serve  as  poles  of  the  battery. 

c.    Electro- Motive  Force  of  Batteries. 

370.  Apparatus.  —  Same  as  in  the  last  section. 

371.  Exercise.  —  Measure  the   electro-motive  force  of   a 
battery. 

For  this  experiment  there  will  be  needed  a  battery  giving 
a  constant  current  whose  E.  M.  F.  is  known.  For  most  pur- 
poses, that  is,  wherever  great  accuracy  is  not  required,  the 
Daniell' s  cell  may  be  used.  If  the  liquids  of  this  battery  are 
solutions  of  zinc  sulphate  and  copper  sulphate  of  the  same 
density,  then  its  E.  M.  F.  is  about  1.1  volt. 

First  Method.  —  Connect  in  circuit  with  the  cell  serving 
as  a  standard  a  set  of  resistance  coils  and  a  galvanometer. 
Now  introduce  through  the  resistance  coils  a  resistance  of 


216  PRACTICAL  PHYSICS. 

R  ohms  and  read  the  deflection  a  of  the  galvanometer.  Then 
substitute  the  cell  whose  E.  M.  F.  is  to  be  determined  for  the 
standard  cell,  and  adjust  the  resistance  R'  so  as  to  obtain  the 
same  deflection  of  the  galvanometer  as  before.  Hence,  as  the 

1  ' 

currents   are   equal  in   the  two    cases, 


-  , 
B'+r'+g' 

and   E'  =  .  E   in   which   E    and    E'  represent    the 


E.  M.  F.  of  the  standard  cell  and  the  unknown  one  respectively. 
By  making  R  and  R'  large,  then  r  and  r'  may  be  neglected 


without  sensible  error,  and  E'  =  .JJ,  that  is,  the  E.  M.  F. 


of  the  two  cells  are  proportional  to  the  resistances  which  produce 
equal  deflections  of  the  galvanometer.     Multiplying  the  value 

B'+  g 
of  E  by   £    .        gives  the  E.  M.  F.  of  the  cell  under  examina- 

tion. 

By  employing  large  resistances  and  a  sensitive  galvanometer 
better  results  will  be  obtained  as  polarization  is  retarded. 

Second  Method.  —  Connect  in  circuit  the  standard  cell,  the 
tangent  galvanometer,  and  the  resistance  coils.  Introduce 
sufficient  resistance  R  to  give  a  deflection  a,  something  between 
20°  and  50°.  Now  substitute  for  the  standard  cell,  the  one  of 
unknown  E.  M.  F.,  and  adjust  the  resistance  R7  so  that  the  total 
resistance  of  the  circuit  is  the  same  as  when  the  standard  cell 
was  used,  and  record  the  deflection  a'.  This  will  require  that 

E 

r,  r',  and  g  be  known.     By  Ohm's  law  we  have  C  —   ^   .  —  -r— 

E'  C       E 

and   C'=  -nT~\  —  7~\  —  '  whence  -77-,  =  ~wi">    as    the    denominators 

~ 


C       tan  a 
were  made  equal.    By  the  law  of  the  galvanometer  ~7T?  —  /  -  1' 

Hence  E  '  =  E  ---      By  using  a  sensitive  galvanometer  of 
tan  a 


MAGNETISM  AND  ELECTRICITY.  217 

several  thousand  ohms  resistance  the  resistance  coils  may  be 
omitted  and  the  resistance  of  the  battery  neglected. 

Third  Method.  —  Connect  in  circuit  with  a  galvanometer 
and  a  set  of  resistance  coils  the  weaker  of  the  two  cells, 
the  standard  and  the  unknown.  When  a  resistance  R  is  used 
record  the  deflection  a  of  G.  Then  add  resistance  R'  to  reduce 
the  galvanometer  reading  any  convenient  number  of  degrees, 
as  10°.  The  galvanometer  should  be  adjusted  to  give  a  deflec- 
tion in  the  vicinity  of  45°.  Now  exchange  batteries  and 
introduce  such  resistance  R"  as  to  produce  the  same  deflec- 
tion a.  Then  add  enough  more  resistance  R'",  to  reduce 
the  deflection  the  same  number  of  degrees  as  before. 

R"' 

From  Ohm's  law  it  follows  that  E'  =  ^  -E,  that  is,  the  E.  M. 

F.  of  two  cells  are  to  each  other  as  the  resistances  which  pro- 
duce equal  diminutions  of  current  strength. 

E 

Proof    of    the    above    rule  :    C  =  -p—  7      ,     »  when    a    was 

•K    r  r  T"  9 

first     observed.      On     reducing     this     deflection     10°,     then 

E 

C  '  =  p  .    p-fi  -  j  —   As  the  deflection  was  made  the  same  when 
-\-r-\-g 


the  stronger  battery  was  used  then  the  current  strength  was  the 

E' 
same  and  C  =  ^7,  ,   r/>     •    On    reducing  this   deflection    10°, 

E' 

as  before,  then  Cr/==-^7T,    jgw  rrx"*  R'"   being   the    extra 


resistance    required  to   bring  about    the    necessary  reduction. 

E  E1  E 

Therefore,    p  .       .   „  =  p,,  .  ..n~*    and 


E' 

ft"  I  7?^"T — ~\~~ '     ^   ^ne  mem^ers  °^    these   equations   are 

inverted  and   the   resulting   equations   subtracted    from    each 


218  PRACTICAL  PHYSICS. 

E'       R'" 

other,    member    from  member,    we    have   -^r  =  ^  ,  whence 

Mi  ±Li 


In  measuring  the  E.  M.  F.  of  batteries  which  polarize  rap- 
idly, as  the  Leclanche,  or  whose  E.  M.  F.  falls  rapidly 
on  closing  the  circuit,  as  the  chromic  acid  battery,  the  ad- 
justments  required  by  the  above  methods  must  be  approxi- 
mated to  at  first  and  the  battery  then  allowed  to  rest  for  a  few 
moments  to  recuperate.  After  that  the  circuit  may  be  again 
closed  and  the  former  approximations  corrected  as  rapidly, as 
possible.  A  few  trials  will  lead  to  very  satisfactory  results. 
It  is  well  to  remember,  however,  that  the  E.  M.  F.  of  a  battery 
changes  somewhat  with  the  resistance  of  the  circuit. 

372.  Exercise.  —  Determine  whether  the  E.  M.  F.  is  af- 
fected or  not  by  the  size  of  the  plates. 

373.  Exercise.  —  Measure  the  E.  M.  F.    of    a   cell   and 
compare  it  with  that  of  two  cells  of  the  same  kind  when  joined 
abreast.     Also   compare   it  with  that  of  two  when  joined  in 
series.     Inference. 

374.  Exercise.  —  Calibrate,  any  galvanometer  so  that  its 
readings  will  be  those  of  a  tangent  galvanometer. 

^Connect  in, circuit  a  tangent  galvanometer,  G,  the  galvanoiu-. 
eter  to  be  calibrated,  G',  a  set  of  resistance  coils  and  a  con- 
stant battery.  Now  introduce  sufficient  resistance  to  reduce 
the  deflection  of  G'  to  1°,  and  read  G,  then  lessen  the  resist- 
ance till  G'  =  2°,  and  read  G,  and  so  on  till  the  equivalents  of 
about  50°  have  been  obtained. 

If  the  resistance  is  reduced  to  zero  before  a  deflection  of  45° 
is  reached,  then  increase  the  current  by  introducing  a  second 


MAGNETISM  AND  ELECTRICITY. 


219 


cell,  repeating  the  observations  for  the  last  galvanometer  de- 
flection observed  when  the  single  cell  was  employed  in  order 
that  the  ratio  sustained  by  the  new  readings  to  the  old  may  be 
obtained  and  all  reduced  to  the  one  standard. 

If  the  two  galvanometers  are  so  different  in  sensitiveness 
that  a  current  which  causes  a  large  deflection  of  one  produces 
but  little  effect  on  the  other,  then  connect  the  terminals  of  the 
more  sensitive  one  by  a  wire,  called  a  shunt,  so  that  only  part 
of  the  current  passes  through  the  galvanometer.  A  galvanom- 
eter calibrated  in  this  way  must  be  used  in  connection  with 
the  shunt  employed  in  calibrating  it,  whenever  its  readings  are 
to  be  used  in  comparison  with  this  particular  tangent  galvanom- 
eter. When  used  alone  the  shunt  may  be  dropped  and  the 
calibrated  readings  will  be  those  of  a  tangent  galvanometer. 

375.  Exercise.  —  Determine  the  law  for  divided  electrical 
circuits,  that  is,  if  two  conductors  join  two  points  of  a  battery 
circuit,  find  how  the  current  in  each  branch  is  related  to  "the 
resistance  of  that  branch. 

Set  up  a  circuit  as  shown  in  Fig.  154,  consisting  'of  four 
galvanometers,  of  known  resist- 
ance, all  calibrated  by  compari- 
son with  the  same  standard,  two 
resistance  coils  and  a  constant  bat- 
tery. Short  thick  wires  should  be 
used  so  that  the  resistance  may  be 
practically  confined  to  the  galva- 
nometers and  the  coils. 

1st.  Set  R  and  Rx  so  that  the 
total  resistance  in  the  branches 
CD  and  EF  are  equal.  Compare 
G  and  G15  G2  and  G3,  G  and  G-j. 
Inference. 


FIG.  154. 


220  PRACTICAL   PHYSICS. 

2d.  Set  R  and  Rx,  so  that  the  total  resistance  in  EF  is 
twice  that  in  CD.  Compare  as  before.  Inference. 

3d.  Set  R  and  R1?  so  that  the  total  resistance  in  EF  is 
three  times  that  in  CD.  Compare  as  before.  Inference. 

Frame  a  law  expressing  the  conclusions  reached. 

376.  Exercise.  —  Calibrate  any  galvanometer  so  that  the 
relative  current-strengths  are  known,  and  hence  the  absolute 
strengths,  provided  the  value  in  amperes  of  any  one  reading  is 
known. 

Connect  in  circuit  a  constant  battery,  two  sets  of  resistance 
coils  and  a  galvanometer  (Fig.  155). 
If  MI  =  g,  then  half  of  the  current  goes 

through  G.      If  MI  =  -|,  then  a  third  of 

the  current  goes  through  G.     If  Rl  =  ^ 
then  a  fourth  of  the  current  goes  through 

G.     If  Ri=-^-,  then   ith   of    the  cur- 
n-l  n 

FIG.  155. 

rent  goes  through  G. 

As  the  shunt  reduces  the  total  resistance  of  the  circuit,  to 
maintain  the  current  constant  a  suitable  compensation  must  be 
introduced  each  time  by  means  of  R.  To  determine  the  amount 
of  this  compensation  it  is  evident  that,  as  the  conductivity  of 

the  galvanometer  and  the  shunt  circuit  combined  is  —  J = 

9        #1 

^-  *,  the  combined  resistance  of  these  circuits  is  — —. — —• 

gfii  g+  RI 


As  .#= 


9  then        ,    *      =  :L>    Hence  the  compensation  to 


n-l'  g  + 

g  n—\ 

be  added  is    g  -  —  ==  g.  — . 

H  71 


MAGNETISM  AND  'ELECTRICITY.  221 

When  n  =  2,  Rl  =  gr,  the  current  in  G  is  one-half,  and  the 
compensating  resistance  is  £  g. 

When  n  =  3,  R±  =  2  gr,  current  =  £,  compensating  resistance 

=!?• 

When  n  =  4,  ^  =  3  #,  current  =  £,  compensating  resistance 

=  !</• 

When  n  =  5,  Rl  =  4  gr,  current  =  |,  compensating  resistance 

*>§. 

Hence,  if  we  put  in  the  circuit  the  ^-shunt,  and  through  R 
the  compensation  -J  #,  then  add  resistance  through  R  sufficient 
to  produce  a  deflection  of  1°,  on  removing  the  shunt  and  the 
compensating  resistance  the  current  through  G  will  be  doubled. 

If  this  deflection  is  recorded  it  will  indicate,  whenever  it  is 
obtained,  that  the  current  then  flowing  is  double  that  which 
gave  the  deflection  of  1°. 

Now,  try  in  succession  the  •jpshiint,  J-shunt,  etc.,  with  the 
proper  compensating  resistances,  as  determined  above,  and 
deflections  for  three  times,  four  times,  etc.,  the  current  at  1° 
will  be  sent  through  the  galvanometer.  Tabulate  these  deflec- 
tions and  the  calibrated  scale  for  relative  current  strengths  will 
be  known. 

XIII.      ELECTRO-MAGNKTISM   AND    ELECTRO-DYNAMICS. 

377.  Apparatus.  —  Batteries,  Iron  Filings,  Insulated  Wire, 
Bar  Magnet,  Electro-Magnet,  Ampere  App.,  Magnetoscope,  Float- 
ing Battery,  Sounder,  Telegraph  Key,  Relay,  etc. 

378.  Exercise.  —  Connect  two  or  more  large  cells,  in  par- 
allel circuit,  with  short  thick  wire.     Close  the  circuit  through  a 
heavy  wire,  and  then  dip  a  portion  of  it  into  iron  filings.     Com- 
pare the  result  with  that  obtained  when  the  wire  is  carrying 
no  current. 


222 


PEACTICAL   PHYSICS. 


379.  Exercise.  —  Thrust  the  wire  of  the  last  experiment 

vertically  through  a  sheet  of  stiff 
paper  supported  in  a  horizontal 
position  (Fig.  156).  After  closing 
the  circuit  sift  a  few  iron  filings 
on  the  paper,  jarring  it  slightly 
with  the  finger  as  they  fall.  Com- 
pare the  figure  with  that  given 
when  the  wire  carries  no  current. 

VCJM 

Inference. 

FIG.  156. 

380.  Exercise.  — Coil  into  flat  spirals,  8  cm.  in  diameter, 
some  No.  20  insulated  copper  wire,  securing  the  wire  in  place 
by  means   of   sealing-wax   (Fig.    157). 

Suspend  these  from  two  wire  hooks, 
fixed  to  a  piece  of  board  and  con- 
nected to  binding-posts,  the  hooks 
being  placed  so  that  the  coils  hang  par- 
allel and  about  1  cm.  apart.  The 
lower  ends  of  the  wires  clip  into  a  vessel 
of  mercury  to  a  depth  of  1  mm.  Now 
pass  a  current  from  a  chromic  acid,  or 
Bunsen  cell,  through  these  coils,  by  join- 
ing the  battery-poles  to  the  posts  on  the 
board,  and  record  the  effect.  Turn  one 
of  the  spirals  over,  and  again  record  the 
effect.  Trace  the  direction  of  the  cur- 
rent through  the  spirals,  in  each  case, 
and  devise  a  law  embodying  the  results. 

Straight  wires  may  be  substituted  for  the  spirals  ;  then,  if  the 
battery-poles  are  connected  to  the  posts,  the  current  will  move 
in  opposite  directions  in  the  two  wires  :  and  if  one  battery-pole 


FIG.  157. 


MAGNETISM  AND  ELECTRICITY.  223 

is  joined  to  both  posts  and  the  other  pole  is  connected  to  the 
mercury-cup  the  currents  will  have  the  same  direction.  A 
battery  of"  several  cells  joined  abreast  will  be  necessary  when 
straight  wires  are  employed. 

381.  Exercise.  —  Thrust  the  straight  part  of  the  wires  of 
the  last  experiment  through  a  sheet  of  paper  supported  horizon- 
tally, and  study  the  magnetic  field,  as  in  Art.  379  ;  first,  when 
the  current  in  the  wires  have  the  same  direction  ;  and  secondly, 
when  opposite.     Test  the  effect  of  increasing  the  current  by 
increasing  the  number  of  cells.     How  would  you  join  them? 

382.  Exercise.  —  Determine   the  laws   of  electrical  cur- 
rents. 

Construct  a  rectangular  frame,  25  cm.  square,  out  of  insu- 
lated copper  wires,  No.  20,  by  winding  about  four  layers  around 
the  edge  of  a  square  board.     Slip  the  wire  off  the  board,  and 
tie  the  parts  together  in  a  number  of  places  with  fine  cord. 
Bend  one  end  of  the 
wire    into    a    hook- 
form     (Fig.     158), 
the  other  end  to  be 
left     straight,     ex- 
tending   out    from 
the  other  side.  Bend 
a  narrow    strip   of 
bniss  into  n  J-form, 
giving    the    hooked 
part  a  spoon-shape, 
so  that  it  will  hold 
a  small  globule  of 
mercury.      Support 
the  strip   in   a   bu-  FIG-  158. 


224  PRACTICAL   PHYSICS. 

rette-holder,  and  hang  the  rectangle  from  it  with  the  straight 
end  dipping  into  a  vessel  of  mercury.  Adjust  the  shape  of 
the  hooked  part  of  the  wire  so  that  the  upper  and  lower  sides 
of  the  rectangle  are  horizontal,  the  frame  keeping  any  position 
given  it,  and  turning  on  application  of  the  slightest  force. 
The  supporting  point  of  the  frame  should  be  conical,  good 
contact  being  secured  by  a  globule  of  mercury.  Connect  one 
pole  of  the  battery  to  the  strip,  and  the  other  to  the  vessel  of 
mercury. 

Wind  four  or  five  layers  of  insulated  wire  around  the  edge 
of  a  board  20  cm.  by  10  cm.  Connect  this  in  the  same  cir- 
cuit with  EF,  support  it  near  to  EF  and  in  the  same  plane, 
with  the  current  moving  through  it  parallel  to  that  in  F, 
and  in  the  same  direction,  and  record  the  effect  on  EF.  In- 
ference. 

Remove  HK  from  the  circuit,  and  hold  a  bar  magnet  parallel, 
to  EF,  or  place  it  beneath  it  and  in  the  same  plane,  and  record 
the  effect.  Reverse  either  the  magnet  or  the  direction  of  the 
current,  and  again  record  the  effect.  What  law  seems  to  gov- 
ern the  phenomenon  ? 

Coil  some  No.  16  insulated  wire  into  a  close  spiral  (Fig.  159), 
arranging  it  for  suspension  in  the  same  manner  as  in  the  case 

of  the  wire  rectangle.  Give 
the  spiral,  usually  called  a  Sole- 
noid, a  diameter  of  4  cm.  and  a 
length  of  15  cm.  Suspend  the 
solenoid  in  place  of  the  wire 
frame,  adjusting  it  so  that  it 
hangs  horizontally  and  turns 
FlG>  159>  freely  on  its  support.  Close  the 

circuit,  and  then  hold  a  strong  magnet  near  one  of  its  ends. 
Determine  the  effect  of  reversing  the  current.  Trace  the  current 


MAGNETISM  AND  ELECTRICITY. 


225 


FIG.  160. 


through  the  solenoid.      In  what  direction  is  it  moving  in  the 
N-seeking  end? 

Apply  the  law  derived  from  the  study  of 
the  solenoid  to  an  Electro-Magnet  (Fig. 
160)  to  determine  its  polarity  when  in  cir- 
cuit with  a  battery.  Test  the  conclusion 
reached  by  placing  it  in  a  battery  circuit 
and  bring  its  poles  in  succession  near  a 
magnetoscope. 

Double  part  of  the  wire  of  the  circuit 
back  on  itself  as  shown  in  Fig.  161,  and 
hold  it  parallel  to  one  of  the  vertical  sides 

of  the  suspended  wire  rectangle.  Account  for  the 
lack  of  motion  on  the  part  of  the  rectangle. 
Use  a  strong  current. 

Substitute  for  the  simple  loop  a  spiral,  with 
the  return  wire  passing  in  a  straight  line  through 
it  (Fig.  161).  Compare  the  result  with  that 
obtained  in  the  last  case.  Is  the  action  of  the 
sinuous  portion  any  greater  than  that  of  the  rec- 
tilinear ?  What  must  be  the  effect  on  the  sole- 
noid to  have  the  wire  bent  parallel  to  its  axis,  as 
shown  in  Fig.  159? 

Mount  a  magnetic  needle  so  as  to  be  free  to 
move  in  any  direction  in  a  horizontal  plane. 
Hold  parallel  to  the  needle,  and  a  little  above 
it,  a  wire  carrying  an  electric  current  of  known  direction,  and 
record  the  effect.  Compare  this  with  the  solenoid  when  an 
electric  current  passes  parallel  to  its  axis,  above  it,  and  in  the 
same  direction  with  respect  to  the  line  joining  its  poles,  as  it 
did  in  the  case  of  the  magnet.  Try  the  current  below  in  each 
case.  Ascertain  the  effect  of  reversing  the  current. 


FIG.  161. 


226  PRACTICAL  PHYSICS. 

383.  Exercise.  —  Make  a  small  chromic  acid  battery,  using 
a  short  wide  test- tube,  or  a  light  bottle,  for  a  battery- jar.    Insert 

it  in  a  cork  of  sufficient  size  to  float  the 
apparatus  in  a  vessel  of  water  (Fig.  162). 
Connect  the  poles  of  the  battery  with  a 
small  helix  of  wire.  Float  the  apparatus 
in  a  vessel  of  water,  and  observe  if  it 
assumes  any  one  position  in  preference  to 
another.  Hold  a  straight  wire  forming 
part  of  a  battery-circuit  parallel  to  the 

axis  of  the  helix.  Record  the  effect.  Hold  a  pole  of  a  perma- 
nent magnet  near  one  end  of  the  helix.  Record  the  effect. 
Frame  a  law  expressing  the  action  of  electric  currents  on  each 
other,  as  well  as  the  action  of  currents  on  magnets,  as  proved 
by  this  floating  battery. 

If  the  edges  of  the  cork-float  are  greased,  there  will  be  less 
tendency  on  the  part  of  the  apparatus  to  keep  against  the  side  of 
the  vessel,  especially  if  the  latter  is  filled  to  the  brim  with  water. 

384.  Exercise.  —  Set  up  a  telegraph  line,  the  longer  the 
better.     A  return  wire  may  be  used,  or  the  wires  may  be  con- 
nected to  the  gas-pipes,  if   rooms   in  the  same  building  are 
joined.     If  distant  buildings  are  connected,  the  earth  may  be 
used  for  the  return  circuit.    In  that  case  earth  connections  may 
be  secured  by  connecting  the  wires  to  the  gas  or  water  pipes,  if 
possible,  or  to  large  metal  plates  buried  deep  enough  to  reach 
moist  earth.     If  the  line  is  set  up  within  a  room,  a  coil  of  Ger- 
man-silver wire  may  be  put  in  circuit  to  make  the  line  resemble 
a  long  one.     In  any  case  the  insulation  of  the  line  must  be 
secured.     Measure  the  resistance  of  each  instrument  and  also 
of  the  complete  line.     Connect  a  sounder,  a  relay,  and  a  set  of 
resistance  coils  in  the  line,  and  compare  their  working  as  the 


MAGNETISM   AND    ELECTRICITY. 


227 


resistance  of  the  line  is  increased  by  connecting  in  more  wire. 
Determine  the  current  required  to  work  the  relay ;  also  that 
required  to  work  the  sounder. 

XIV.    CURRENT    INDUCTION. 

385.  Apparatus.  —  Galvanometer,    Battery,     Helices    of 
Wire,  Electric  Motor,  Bar  Magnet,  Microphone,   Coils  of  Insu- 
lated Wire,  Sheets  of    Rubber,  Copper,  Paper,    Zinc,  and  Iron, 
Induction  Coil,   Telegraph  Key,  etc. 

386.  Exercise.  —  Wind  smoothly  a  few  layers  of  insulated 
copper  wire,  No.  24,  on  a  hol- 
low paper  or  wooden  cylinder 

with  thin  walls  (Fig.  163). 
Connect  this  helix  with  a  sen- 
sitive galvanometer.  Now  in- 
troduce suddenly  into  the  helix 
the  N-seeking  pole  of  a  strong 
bar  magnet.  Why  is  the 
needle  deflected?  What  di- 
rection must  the  current  have 
had?  Is  there  any  current 
when  the  magnet  is  stationary 
within  the  coil  ?  Suddenly  remove  the  magnet  and  compare 
the  effect  with  that  previously  obtained.  Try  the  S-seeking 
pole.  Try  magnets  of  different  strengths.  Try  a  helix  having 
less  wire.  Conclusions. 

387.  Exercise.  —  Place  within  the  helix  used  in  the  last 
experiment  a  soft  iron  core,  consisting  of  a  number  of  No.  18 
iron  wires,  the  length  of  the  spool.     Now  move  the  pole  of  a 
strong  bar  magnet  suddenly  up  to  the  end  of  this  core,  and  ob- 
serve the  effect  on  the  galvanometer.     Try  moving  the  pole  of 
the  magnet  rapidly  away  from  the  core.    Trace  out  the  currents 


FIG.  1€3. 


228  PRACTICAL    PHYSICS. 

produced  in  the  helix,  and  compare  their  direction  with  the 
Amperian  currents  of  the  magnet. 

388.  Exercise.  —  Connect  an  Elec- 
tric Motor  (Fig.  164)  to  a  sensitive 
galvanometer  of  low  resistance.  Ro- 
tate the  armature  of  the  machine  by 
rapidly  pulling  off  a  string  wound  on 
the  shaft.  Observe  the  effect  on  the 
galvanometer.  Reverse  the  direction  of 
rotation.  Explain  the  action  of  the 
machine  in  the  light  of  the  laws  of  in- 
duction developed  in  Art.  386. 

389.  Exercise.  —  Wind  on  a  paper  bobbin,  2  cm.  long, 
about  30  g.  of  No.  30  insulated  copper  wire,  and  place  it  around 
the  pole  of  a  bar  magnet,  supported  horizontally  (Fig.  165). 
Connect  the  terminals  of  the  helix  to  a  sensitive  galvanometer. 
Cut  out  of  thin  sheet-iron,  such  as  photographers  use  in  "  tin- 


FlG.  165, 

typing,"  a  disk  8  cm.  in  diameter.  Cement  to  it  a  wooden 
handle.  Now  move  the  disk  suddenly  toward  the  pole  of  the 
magnet  and  observe  the  effect  on  the  galvanometer.  Try 
moving  it  suddenly  away  from  the  pole.  Explain. 

Replace  the  galvanometer  by  a  second  bobbin  and  magnet 
(Fig.    166).     Opposite  the  pole  of  the  second  magnet  and  near 


MAGNETISM    AND   ,ELECTEICITY. 


229 


to  it  suspend,  by  a  thread,  an  iron  disk  to  the  centre  of 
which  is  cemented  a  piece  of  mirror.  Place  the  apparatus 
where  a  ray  of  sunlight  may  strike  the  mirror  and  be  reflected 
on  the  wall.  Now  move  the  first  disk  in  the  same  manner  as 


FIG. 166. 

when  the  galvanometer  was  in  circuit,  and  observe  the  effect 
on  the  second  disk  by  means  of  the  spot  of  light  on  the  wall. 

The  apparatus  will  be  more  sensitive  if  the  edge  of  the  disk 
is  opposite  the  pole  of  the  magnet,  for  then  it  will  turn  on  a 
vertical  axis. 

Bell  telephone  receivers  may  be  substituted  for  the  magnets 
and  bobbins  employed  above. 

390.  Exercise.  —  Fasten 
two  square  pieces  of  gas-carbon 
to  an  upright  strip  of  thin 
wood,  and  join  them  by  a  car- 
bon pencil  with  tapering  ends, 
resting  loosely  in  conically 
shaped  cavities  in  the  horizon- 
tal bars  (Fig.  167).  Place  this 
Microphone*  in  circuit  with  a 
battery  and  a  Bell  telephone  by 

FIG.  167. 


*  The  Microphone  does  not  illustrate  Current  Induction.     Its  consideration  at  thia 
point  is  found  convenient  on  account  of  using  it  in  connection  with  the  Telephone. 


230 


PEACTICAL    PHYSICS. 


twisting  wires  around  the  horizontal  bars.  Listen  through  the 
telephone  to  the  ticking  of  a  watch  resting  on  the  base  of  the 
microphone.  Connect  two  rooms  electrically,  the  microphone 
and  telephone  being  in  the  circuit,  but  in  different  rooms. 
Listen  at  the  telephone  to  the  talking  of  an  assistant  standing 
near  the  microphone. 


391.  Exercise.  —  Insert  within  a  helix  connected  with  a 
galvanometer  a  second  helix  in  cir- 
cuit with  a  battery  (Fig.  168).  Ob- 
serve the  effect  of  introducing  or 
removing  suddenly  this  helix.  Try 
opening  or  closing  the  circuit  without 
moving  the  helix.  Set  up  the  appa- 
ratus with  a  set  of  resistance  coils  in 
the  battery  circuit.  Ascertain  the 
effect  of  weakening  or  strengthening 
the  current  by  varying  the  resistance. 
Reverse  the  direction  of  the  battery 
current  and  repeat  the  tests.  Write 
a  law  describing  the  direction  of  the 
induced  currents  as  compared  with  the 
FIG.  168.  battery  current. 


392.  Exercise.  —  Construct  two  large  flat  coils  of  in- 
sulated copper  wire  No.  24.  Place  one  of  them  in  circuit 
with  a  battery  and  some  form  of  current  breaker,  as  a  tele- 
graph key,  and  the  other  in  circuit  with  a  sensitive  galvanom- 
eter. Lay  one  of  these  coils  on  the  other  on  the  table,  with 
a  sheet  of  cardboard  between  them.  Read  the  galvanometer 
on  closing  the  circuit  and  also  on  opening  it.  Substitute  a 


MAGNETISM    AND    ELECTRICITY. 


231 


sheet  of  india-rubber  for  the  paper.     Try  a  sheet  of  copper. 
Try  a  sheet  of  zinc.     Try  a  sheet  of  iron.     Inference. 

393.  Exercise.  —  Connect  one  pole  of   a  battery  with  a 
file,  and  draw  across  its  rough  surface  the  wire  attached  to  the 
other  pole.     Observe  the  intensity  and  the  color  of  the  sparks. 
Repeat  the  experiment  after  introducing  into  the  circuit  a  helix 
of  wire.     Explain.      Place  an  iron  core  in  the  helix,  and  re- 
peat.    Explain. 

394.  Exercise.  —  Connect  the  secondary  coil  of  a  small 
induction  coil  with  a 

galvanometer,  and 
the  primary  coil  with 
a  battery  (Fig.  169). 
Read  the  galvanom- 
eter on  closing  the 
circuit  and  also  on 
opening  it.  Repeat 
the  observations  af- 
ter removing  the  iron  FIG  16Q 
core.  Explain. 

Remove  the  galvanometer,  and  test  the  differences  in  the 
induced  currents  by  the  physiological  effects  experienced  on 
holding  the  wires  in  your  hands. 

The  helices  of  Art.  391  may  be  used  for  the  above  experi- 
ment. 

395.  Exercise.  —  With  a  battery,  a  long  coil  of  wire,  a 
sensitive  galvanometer,  and  a  telegraph  key  set  up  a  circuit 
as  shown  in  Fig.  170. 

On  closing  the  circuit  the  needle  is  deflected  by  a  part  of  the 


232  PRACTICAL    PHYSICS. 

current  passing  through  the  galvanometer.      Now  bring  the 

needle  back  to  zero,  and 
place  some  impediment  in 
the  way  so  it  cannot  move 
in  that  direction,  but  is  free 
to  swing  in  the  opposite. 
Break  the  current,  and 
account  for  the  needle's 

Fl^.  170.  , 

moving    in    the    opposite 

direction  to  that  in  which  the  battery  current  would  cause  it  to 
move. 

396.  Exercise.  —  Connect  one  pole  of  the  secondary  coil 
of    an  induction   coil,  giving  a  spark    at  least  2  cm.  long,  to 
one  surface  of  a  Leyden  jar,  and  the  other  pole  to  the  other 
surface.     Observe  the  effect  on  the  spark  given  by  the  coil. 

397.  Exercise.  —  Around  the  edge  of  a  wooden  barrel- 
hoop  wind  several  layers  of  No.  24  insulated  wire,  fastening 
the  wire  in  place  by  tying   it  in   several  places  with   cords. 
Leave  the  ends  of  the  wire  quite  long,  and  connect  them  with 
an    astatic    galvanometer  of    low    resistance.      Now  hold  the 
coil  in  both  hands  in  a  plane  at  right  angles  to  the  direction 
of    the    dipping-needle,   and   quickly    rotate   it   through    180° 
around  a  horizontal   axis  lying  east  and  west.     Observe  the 
effect  on  the  galvanometer.     Try  the  effect  of  rotating  the  coil 
in  the  opposite  direction.     Explain. 

Ascertain  if  there  is  any  induction  when  the  axis  of  rotation 
is  horizontal  and  in  the  magnetic  meridian.  Try  the  axis  par- 
allel to  the  dipping-needle. 

If  such  a  hoop  is  mounted  on  an  axis  provided  with  a  crank 
for  rapid  rotation,  the  wires  being  connected  to  a  commutator 
on  the  axis,  quite  marked  electrical  effects  are  easily  obtained. 


MAGNETISM   AND    ELECTRICITY. 


233 


XV.    LUMINOUS    EFFECTS. 

398.  Apparatus.  —  Tin-Foil,  Panes  of  Glass,  Plates  of  Mica, 
Aurora-Tube,  Air-Pump,  Glass  Goblet,  Geissler's  Tubes,   etc. 

399.  Exercise.  —  Cut  with   a   small   punch  a  number  of 
circular  pieces  of  tin-foil,  and  paste  them  on  a  pane  of  glass,  a 


FIG.  171. 

fish-globe,  a  glass  tube,  or  a  Ley  den  jar  without  an  outer  coat- 
ing, forming  any  desired  pattern  (Figs.  171,  172).  The  edges 
of  these  disks  should  be  about  1  mm.  apart.  Con- 
nect the  poles  of  an  induction  coil  or  of  an  electrical 
machine  witli  the  extremities  of  the  design  and  pass 
electric  sparks  through  it,  conducting  the  experiment 
in  a  dark  room. 


400.  Exercise.  —  Paste  on  a  plate  of  mica  about 
15  cm.  by  10  cm.,  a  piece  of  tin-foil  8  cm.  by  5  cm. 
Support  it  on  a  plate  of  glass  with  the  mica  surface 


FlG-  "2. 


234 


PRACTICAL    PHYSICS, 


out,  and  bring  the  poles  of  an  electrical  machine  or  induction 
coil  within  1  cm.  of  the  surface,  the  distance  between  them  not 
exceeding  the  length  of  the  tin-foil.  Set  the  machine  in  opera- 
tion, darken  the  room,  and  observe  the  path  of  the  spark  across 
the  mica  plate. 

401.  Exercise.  —  Substitute  for  the  mica  plate  of  the  last 
experiment  a  plate  of  glass,  covered  with  iron-filings,  and  hav- 
ing a  narrow  strip  of  tin-foil  pasted  across  the  two  ends  beneath 
the  poles  of  the  machine.     To  make  the  filings  adhere,  coat  the 
plate  with  mucilage,  sift  on  evenly  the  filings,  and  set  away  to 
dry. 

402.  Exercise.  —  Exhaust   the  air  from  the  Aurora- Tube 


\      9 


FIG.  173. 


FIG.  174. 


(Figs.  173,  175),  and  connect  the  extremities  to  the  poles  of  an 
active  electrical  machine  or  induction  coil.     Study  its  appear- 


MAGNETISM   AND    ELECTRICITY.  235 

ance  in  a  darkened  room.     Note  the  effect  of  reversing  the 
current. 

Substitute  for  the  aurora-tube  the  apparatus  shown  in  Fig. 
174,  where  the  mouth  of  a  bell  jar  is  closed  with  a  Florence 
flask,  on  which  is  pasted  tin-foil,  covering  two-thirds  of  the 
bulb.  A  brass  chain  hangs  within  the  flask,  touching  the  inner 
surface.  One  pole  of  the  electrical  generator  is  connected  to 
the  brass  chain,  and  the  other  to  the  plate  of  the  air-pump. 
Observe  the  effect  in  a  dark  room,  as  the  air  is  exhausted  from 
the  bell-jar. 

403.  Exercise. — Coat  a  glass  goblet  inside  and  outside  with 
tin-foil   (Fig.  176)   a  little  over  half-way  up, 

and  place  it  on  the  table  of  the  air-pump,  be- 
neath a  bell-jar  provided  with  a  brass  sliding- 
rod  passing  air-tight  through  the  cork  of  the 
jar.  Over  that  part  of  the  rod,  within  the  jar, 
secure  a  glass  tube,  adjusting  the  apparatus 
so  that  the  rod  touches  the  bottom  of  the  inner 
surface  of  the  goblet.  Connect  the  rod  and  the 
air-pump  table  to  the  poles  of  an  active  induc- 
tion coil  or  Holtz  machine,  and  then  exhaust 
the  air.  Conduct  the  experiment  in  a  dark  FlG- 176- 
room. 

The  best  effects  are  given  by  a  goblet  made  of  uranium  glass. 

404.  Exercise.  —  Exhaust  the  air   from   the   aurora- tube 
(Fig.  175),  introduce  a  gas,   as  oxygen,  hydrogen,  coal-gas, 
etc.  ;  then  exhaust  once  more,  refill  and  again  exhaust,  repeat- 
ing the  operation  for  several  times,  in  order  that  the  tubes  may 
contain  nearly  pure  gas.     Now  proceed  as  in  Art.  402. 

Dealers  in  physical  apparatus  furnish  vacuum  tubes,  or  Geiss- 
ler's  tubes,  containing  rarefied  vapors  of  known  substances  for 


236  PRACTICAL    PHYSICS. 

the  study  of  the  effects  of  the  electrical  discharge  on  the  resid- 
ual gas. 

XVI.    THERMO-ELECTRICITY. 

405.  Apparatus.  —  Strips  of  Zinc,  German-Silver,  Copper, 
Bismuth,  Antimony,  etc.,  and  a  Short-Coil  Astatic  Galvanometer. 

406.  Exercise.  —  Prepare  two  strips,  one  of  zinc  and  the 
other  of  German-silver,   each  5   cm.   long  and  15  mm.  wide. 
Solder  them  together  at  one  end,  and  to  the  free  ends  solder 
wires,  so  as  to  place  them  in  circuit  with  a  sensitive  galvanome- 
ter.    A  short-coil  galvanometer,  having  an  astatic  needle,  is  to 
be   preferred.     Apply  the  flame  of  a   burning   match   to   the 
junction  of  the  two  strips  and  observe  the  effect  on  the  gal- 
vanometer.    Ascertain  the  effect  of  a  piece  of  ice  on  the  junc- 
tion. 

Try  strips  of  copper  and  zinc ;    copper  and  bismuth ;  anti- 
mony and  bismuth.     Compare  the  deflections  given. 

XVII.      SECONDARY   OR    STORAGE    BATTERIES. 

407.  Apparatus.  —  Sheet-Lead,  Red-Lead,    Galvanometer, 
etc. 

408.  Exercise.  —  Cut  out  of  sheet-lead    two  rectangular 
strips,  each  10  cm.  by  12  cm.,  and  tack  them  on  opposite  sides 
of  a  strip  of  dry  wood  2  cm.  thick.    Solder  a  wire  to  each  strip, 
then  dip    the  plates    into    dilute    sulphuric   acid,   and  connect 
them  to  the  poles  of  a  battery  of  sufficient  E.  M.  F.  to  decom- 
pose water.     After  a  few  minutes  disconnect  the  plates  from 
the  battery  and  join  them  to  a  galvanometer  or  small  electric 
motor.     Inference.     Ascertain  whether  the  plates  will  exhibit 
any  electrical  phenomena  or  not,  if  some  little  time  is  allowed 


MAGNETISM   AND    ELECTRICITY.  287 

to  elapse  between  disconnecting  them  from  the  battery  and 
testing  them  with  the  galvanometer. 

409.     Exercise.  —  Cut  out  of  thin  sheet-lead  a  number  of 
plates,  10  cm.  by  15  cm.,  having  on  one  side  an  ear  2  cm.  by  8 
cm.  (Fig.  177).     Cut  out  of  cotton  flannel  twice  as  many  rec- 
tangular pieces,  14  cm.  by  20  cm.     Make 
a  thick  paste  out  of  red-lead  and  sulphuric 
acid,  and  apply  it  with  a  brush  to  both 
sides  of  each  lead  plate,  and  also  to  the 
nap-side  of  the  flannel,  to  a  depth  of  at 
least    1    mm.      Now  build  up  a  battery 
as   follows :     Lay  down  a  piece  of  flan- 
nel, then  one  of  lead,  then  flannel,  then 
blotting-paper  of  the  size  of  the  flannel, 
;then  flannel,  then  a  lead  plate  with  the 

ear  on  the  reverse  side  of  the  last  plate, 

FIG.  177. 

then  flannel,  and  so  on.     Always  place 

the  nap-side  of  the  flannel  next  to  the  lead,  and  be  careful  to 
have  as  many  plates  with  the  ear  on  one  side  as  there  are  plates 
with  the  ear  on  the  other,  consecutive  plates  having  their  ears 
on  opposite  sides.  When  a  sufficient  number  have  been  put  in 
place,  bind  them  together  with  a  cord,  strips  of  thin  board 
being  placed  on  the  outsides.  Wire  together  the  ears  forming 
the  two  poles,  and  place  the  plates  in  a  glass  vessel  containing 
dilute  sulphuric  acid.  To  charge  the  battery,  connect  the  poles 
to  those  of  a  strong  battery  for  an  hour  or  so.  On  disconnect- 
ing the  poles  and  joining  them  to  an  electric  motor  even  after 
the  lapse  of  several  hours  a  rapid  motion  should  be  obtained. 


238  PRACTICAL    PHYSICS. 

CHAPTER    VI 

SOUND. 
I.    WAVE    MOTION. 

410.  Apparatus.  —  Balls,    Whirling-Machine,     Spiral    of 
Spring  Wire,  Cotton  Rope,  Rubber  Tubing,  Rectangular  Trough, 
Tin  Tube,  etc. 

411.  Exercise.  —  Classify  the  following  motions  in  two 
ways,  after  studying  them  closely  to  ascertain  their  points  of 
resemblance  and  of  difference. 

1st.  A  ball  suspended  by  a  thread,  and  set  in  motion  as  a 
pendulum . 

2d.  A  heavy  ball  suspended  by  a  spiral  spring,  made  by 
winding  closely  on  an  iron  rod,  1  cm.  in  diameter,  some  spring 
brass  wire  No.  18,  and  set  in  motion  by  pulling  down  the  ball 
and  then  releasing  it. 

3d.  A  heavy  ball,  suspended  by  a  wire  fastened  to  it,  so  as 
not  to  turn  on  it  as  an  axis,  and  set  in  motion  by  twisting  the 
wire. 

4th.  A  paper  disk  clamped  to  the  axis  of  the  whirling- 
machine,  and  put  in  motion  by  turning  the  drive-wheel. 

5th.  A  weight  with  a  cord  attached,  and  put  in  motion  by 
drawing  it  along  on  the  table. 

6th.  A  wire  stretched  tight,  with  its  ends  secured  by  winding 
them  around  the  heads  of  two  stout  nails  driven  part  way  into 
a  board,  and  put  in  motion  by  pulling  the  middle  of  the  wire  a 
little  out  of  line  and  then  releasing  it. 


SOUND.  239 

412.  Exercise.  —  Place  a  soft  cotton  rope,  5  m.  or  6  m. 
long,  in  a  straight  line  on  the  floor,  fastening  one  end  to  some 
heavy  object.     Holding  the  other  end  of  the  rope  in  the  hand, 
set  up  vibrations  in  it  by  a  quick  movement  of  the  hand  up  and 
down.     Ascertain  the  path  traversed  by  a  point  of  the  rope. 
Compare  the  motion  of  consecutive  points.      Draw  figures  in 
your  note-book  showing  the  form  of  the  rope  at  three  succes- 
sive points  of  time.     Ascertain  the  effect  of  changing  the  time 
in  which  the  hand  makes  its  up-and-down  movement  in  starting 
the  vibration.     Account  for  the  curved  form's  advancing  along 
the  rope. 

413.  Exercise.  —  Fasten  one  end  of  the  rope  used  in  the  last 
experiment,  or,  what  is  better,  a  piece  of  rubber  tubing,  having 
an  outside  diameter  of  1.5  cm.,  to  a  hook  in  the  ceiling  of  the 
room,  and  the  other  end  to  a  hook  in  the  floor  directly  beneath 
it.     Adjust  the  rope  so  that  it  is  under  a  slight  tension.     Strike 
the  rope  with  a  short  rod  at  one-fourth  from  the  bottom,  and 
note  the  action  of  the  pulse  formed.     Just  as  this  pulse  starts 
to  return  from  the  ceiling  start  a  second  one,  and  observe  the 
effect  attending  its  meeting  the  first  one.    Try  striking  the  rope 
one-sixth  from  the  floor.    Draw  figures  showing  the  form  of  the 
rope  at  the  moment  the  pulse  was  started ;  on  its  arrival  at  the 
ceiling  ;  on  its  starting  to  return  ;  and  at  the  time  the  two  pulses 
meet. 

414.  Exercise.  —  Fasten  up  two  similar  ropes  or  tubes  as 
in  the   last   experiment,    subjecting   them   to   equal   tensions. 
Start  pulses  in  them  simultaneously,  and  of  the  same  length, 
and  compare  the  rates  at  which  they  advance  along  the  ropes. 
Now  increase  the  tension  of  one  rope,  and  repeat  the  compari- 
son.    What  force  is  developed  by  stretching  the  rope?     Fasten 


240  PRACTICAL    PHYSICS. 

up  a  third  rope,  much  heavier  than  the  others ;  a  rubber  tube 
filled  with  sand  will  answer.  Compare  the  movement  of 
pulses  in  this  heavy  one  with  similar  pulses  in  the  others. 
Account  for  the  difference.  Increase  the  tension  of  the  heavy 
rope,  and  repeat.  Derive  from  the  observations  made  what 
determines  the  speed  of  propagation  of  the  pulse. 

415.  Exercise.  —  Fill  about  two-thirds  full   of   water  a 
rectangular  trough,  1  m.  long,  30  cm.  deep,  and  10  cm.  wide, 
having  one  side  of   glass.     By  suddenly  depressing  and  elevat- 
ing a  large  bottle  in  one  end  of  the  trough  start  a  wave,  and 
record  the  movement  of  the  water  as  it  appears  through  the 
glass    side.     Start    other  waves,  and    observe  their   behavior 
toward  one    another.     Ascertain  if    one    wave  can  be  started 
so  as  to  increase  the  amplitude  of    the  one  that  preceded  it. 
Try  to  reduce  the  amplitude.     Record  the  conditions  you  had 
•to  observe  in  order  to  accomplish  these  results. 

Float  some  small  paraffine  balls  on  the  water,  and  record  their 
motion  as  the  pulse  travels  along.  In  the  advance  of  the 
wave  is  there  an  advance  of  the  water?  Load  some  of  the 
paraffine  balls  with  iron-filings,  so  that  they  will  float  at  some 
distance  below  the  surface.  Determine  from  the  motions  of  the 
balls  the  character  of  the  motion  of  the  water  particles  when  a 
wave  traverses  the  trough. 

416.  Exercise.  —  Construct  a  spiral  spring,  3  m.  long,  by 
winding  closely  on  a  rod,  1  cm.  in  diameter,  a  quantity  of  No. 
18  spring  brass  wire.     Fasten  one  end  of  this  spiral  to  a  hook 
in  the  wall ;  and,  holding  the  other  end  in  the  hand,  stretching 
the    spiral    till    it   swings    clear   of    the    floor,    send    a    pulse 
through  it  by  pressing  a  few  of  the  coils  of  the  wire    close 
together,  and  suddenly  releasing   them.     Tie  short  pieces  of 


SOUND.  241 

string  into  several  of  the  coils,  and  observe  their  movements  as 
the  pulse  advances.  Describe  the  motion  of  the  parts  of  the 
spiral.  Representing  the  successive  coils  by  a  series  of  short 
parallel  lines,  show  by  a  figure  the  change  in  relative  position 
of  these  lines  in  the  neighborhood  of  a  pulse. 

417.  Exercise. — Place  on  a  table  a  tin  tube,  3  m.  long 
and  10  cm.  in  diameter,  one  end  of  which  tapers  to  a  diameter 
of  2.5  cm.     It  is  preferable  to  have  the  tube  in  parts,  to  be  put 
together  like  stove-pipe.     Tie  over  the  large  end  a  paper  mem- 
brane, and  in  front  of  the  small  end  place  the  flame  of  a  lighted 
candle.     Observe  the  effect  of  slapping  two  books  together  in 
front  of  the  paper  membrane.     Account  for  the  effect  produced 
on  the  flame.     Why  could  it  not  have  been  due  to  a  wind  pro- 
duced by  the  books? 

II.      SOURCES    OF    SOUND. 

418.  Apparatus.  —  Bell,    Tuning-Fork,    Long   Metal  Rod, 
Pane    of    Glass,    Glass   Rod,    Tin   Flageolet,  Tin  Whistle,    Glass 
Tube,  etc. 

419.  Exercise.  —  Strike   a   large   bell    or  glass    bell- jar 
with  a  small  mallet,  made   by  inserting  a  stout  wire   in  a  large 
cork.     Suspend  by  a  thread  a  small  ball  of  pith  or  cork,  so  as 
just  to  touch  the  edge  of  the  bell.     What  do  you  find  to  be  the 
difference  between  a  sounding  bell  and  a  silent  one  ? 

420.  Exercise.  —  Insert  two  large  screw-eyes  in  a  board 
at  points  distant  one-half  of  a  metre.     Stretch  between  them  a 
piece  of  steel  wire,  about  No.  20,  securing  tension  by  turning 
the  screws.      Now  draw  a    violin- bow   across   the   wire,   and 
record  any  attending  phenomenon.     Ascertain  the  condition  of 
the  wire  by  touching  it  with  the  edge  of  a  card.     Inference. 


242  PRACTICAL    PHYSICS. 

421.  Exercise.  —  Tap  a  tuning-fork   against  a  block  of 
wood,  and,  while  sounding,  touch  one  prong  to  the  surface  of  a 
vessel   of   water.      In  what  condition  are   the   prongs  of  the 
fork? 

422.  Exercise.  —  Clamp,  in  a  horizontal  position,  a  metal 
rod,   1  m.  long  and  1  cm.  diameter,  by  its  middle  in   a  vise. 
Suspend  by  a  thread  a  small  ball,  ivory  or  glass,  about  1  cm.  in 
diameter,  so  as  to  rest  gently  against  one  of  the  squared  ends 
of  the  rod.     Rub  the  other  end  of  the  rod  longitudinally  with 
soft  leather,  covered  with  powdered    rosin.      What   does  the 
effect  produced  on  the  ball  indicate  regarding  the  condition  of 
the  rod? 

423.  Exercise.  —  Balance   on   a   small   cork   a   pane   of 
window-glass,  about  25  cm.  square,  and  sprinkle  evenly  over  it 
a  little  fine  sand.     Rest  on  the  glass  plate,  in  a  vertical  posi- 
tion, over  the  centre  of  the   cork,   a  stout  glass  tube  60  cm. 
long.     Hold  this  tube  by  the  upper  end  in  one  hand,  press  it 
firmly  against  the  plate,  and  rub  the  lower  part  longitudinally 
with  a  damp  woollen  cloth  held  between  the  thumb  and  the  fore- 
finger of  the  other  hand.     What  phenomena  attend  the  friction 
of  the  cloth  on  the  tube ?     Are  they  connected?     Inference. 

424.  Exercise.  —  Connect  to  a  faucet  giving  water  under 
considerable  pressure  a  tin  flageolet,  by  means  of  a  rubber  tube 
slipped  over  its    mouth,    but   not   covering   the    embouchure. 
It  will  be  necessary  to  wrap  the  tube  with  wire  to  keep  it  from 
slipping  off.     Place  the  flute  in  a  tall  vessel  of  some  kind,  and 
turn  on  the  water.     By  properly  adjusting  the  water-supply  a 
low  musical   tone   can  be   obtained   on  the   flute's   becoming 
immersed  in  water.     Touch  the  vessel  with  the  hand  while  the 


SOUND. 


243 


FIG.  178. 


flageolet  is  sounding,  comparing  the  sensation  with  that  experi- 
enced when  the  flageolet  is  silent.     Inference. 

425.  Exercise.  —  Insert  a  short  wooden  or  tin  whistle  in 
one  end  of  a  glass  tube  about  30  cm.  long  and  about  2.5  cm. 

in  diameter,  closing  the  other 
end  with  a  cork  (Fig.  178). 
A  suitable  whistle  may  be  ob- 
tained at  any  toy  store.  Dis- 
tribute within  the  tube  a  spoonful  of  fine  cork-dust,  obtained 

by  filing  a  cork.     Hold  the  tube 

in    a    horizontal    position    and 

blow  the  whistle.     Observe  the 

effect  on  the  cork-dust.     What 

must   be  the   condition  of  the 

air  within  the    tube  when   the 

whistle  is  sounding? 

Remove  the  whistle,  place  the 

mouth  to  the  end  of  the  tube,  and 

sing  a  prolonged  note  of  consid- 
erable intensity.  By  trial  a  tone 

can  be  found  which  will  produce 

the  same  effect  as  that  given  by 

the  whistle. 

426.  Exercise.  --  Draw 

out  a  glass  tube  to  a  jet  (see 
page  356).  Connect  it  by  rub- 
ber tubing  to  the  gas-supply, 
support  it  vertically  in  a  clamp, 
light  the  gas  escaping  from  the 
jet,  and  reduce  the  flame  to  the 
height  of  about  2  cm.  Clamp  FIG.  179. 


244  PRACTICAL    PHYSICS. 

over  the  jet  a  glass  tube  with  thin  walls,  about  40  cm.  long  and 
2  cm.  in  diameter  (Fig.  179).  Change  the  position  of  the  jet 
within  the  tube  till  a  musical  note  is  emitted  by  the  tube. 
Compare  the  flame  within  the  tube  when  sounding  with  the 
flame  when  the  tube  is  silent.  Grasp  the  lower  end  of  the  tube 
with  the  hand,  and  compare  the  sensations  produced  by  the 
sounding  tube  with  those  produced  by  the  silent  one.  Oscil- 
late a  small  mirror  back  of  the  flame,  and  compare  the  image 
of  the  flame  when  the  tube  is  silent  with  that  given  when  the 
tube  is  sounding.  Explain. 

III.     TRANSMISSION    OF    SOUND. 

427.  Apparatus.  —  Air-Pump,  Alarm-Clock,  Watch,   Rub- 
ber Tubing,   Tuning-Fork,   Bar  of    Iron,   etc. 

428.  Exercise.  —  Place  under  the  receiver  of  an  air-pump 
a  small   alarm-clock,  separated   from  the  plate   by  a   bed    of 
cotton-wool.     Compare  the  distinctness  with  which  the  sound 
of  the  alarm-bell  is  heard  before  and  after  exhausting  the  air. 
Repeat  the  experiment,  omitting  the  cotton-wool.     Inference. 

429.  Exercise.  —  Place  a  loud-ticking  watch  on  one  end 
of  a  long  strip  of  lath,  and  hold  the  other  end  to  your  ear. 

Compare  the  distinctness 
with  which  you  hear  the 
sound  with  that  when  the 
ear  is  away  from  the  lath. 
Ascertain  the  effect  of 
wrapping  up  the  watch  in 
a  cloth,  and  then  laying  it 
F  on  the  lath.  Inference. 

430.  Exercise.  —  Connect  two  rooms  by  a  wire  or  string 


SOUND,  245 

stretched  between  them  (Fig.  180).  Support  the  wire, 
wherever  needed,  by  passing  it  through  a  loop  made  of  cord. 
The  wire  must  not  touch  any  objects,  nor  turn  any  sharp 
corners.  Connect  each  end  to  the  bottom  of  a  collar-box  or  tin 
cylindrical  can,  by  passing  it  through  a  small  hole,  and  fasten- 
ing it  into  a  button.  Let  an  assistant  talk  near  the  open  end  of 
one  box,  while  you  listen  at  the  other.  Explain. 

431.  Exercise.  —  Fill  a  piece  of  rubber  tubing,  say  2  m. 
long  and  2  cm.   in  diameter,  with  water,    supporting  the  two 
ends  so  that  the  tube  hangs  in  a  curve.     Set  a  tuning-fork  in 
vibration,  and  compare  the  distinctness  with  which  you  hear  the 
sound,  as  an  assistant  holds  the  stem  in  the  water  of   the   tube 
at  one  end,  while  your  ear  is  as  close  as  possible  to  the  other 
end,  with  that  when  the  tube  contains  only  air.     Inference. 

432.  Exercise.  —  Suspend  a  small  bar  of  iron  or  steel  by 
two  strings,  each  1.5  m.  long.     Take  one  string  in  each  hand, 
and,  stooping  over,  press  the  ends  into  the  ears.     Now  let  an 
assistant  strike  the  swinging  bar  with  a  block  of  wood.     Com- 
pare the  distinctness  of  the  sound  heard  through  strings  of  cot- 
ton, linen,  metal,  etc.     Inference. 

IV.     VELOCITY   OF  SOUND. 

433.  Apparatus.  —  Tuning-Fork,     Cylindrical    Jar,     Glass 
Tube,    Rods  of  Glass  and   of  Wood,   etc. 

434.  Exercise.  —  Hold  a  vibrating  tuning-fork,  whose  rate 
is  known,*  over  the  mouth  of  a  cylindrical  jar,  about  35  cm. 
high   and  5  cm.  in   diameter,  and   pour  in   water   slowly,  till 
a  point  is  reached  where  the    sound   is   greatly  strengthened. 

*  A  fork  whose  rate  is  from  250  to  300  will  be  found  to  give  the  best  results.    If  a 
fork  of  higher  pitch  is  used,  then  select  a  cylindrical  jar  of  less  diameter  than  5  cm. 


246  PRACTICAL    PHYSICS. 

Ascertain,  by  repeated  trials,  the  air-column  giving  the  loudest 
resonance,  and  then  determine  its  length.  To  the  length  of  the 
air-column  add  two-fifths  of  the  diameter  of  the  cylinder,  then 
four  times  this  sum  will  be  the  wave-length  for  this  fork.  Mul- 
tiply this  by  the  vibration-number  of  the  fork,  and  the  product 
will  be  the  velocity  of  sound  in  air,  at  the  temperature  of  that 
within  the  cylinder.  Why  ? 

Ascertain  the  effect  that  lowering  the  temperature  has  upon 
the  velocity  of  sound,  by  packing  the  jar  in  melting  ice,  and 
determining  the  air-column  required  for  the  best  resonance,  and 
hence  the  velocity  of  sound  in  this  cooled  air.  Record  the 
temperature  of  the  air. 

A  form  for  keeping  the  record  is  given  below. 

Length  of  resonating  jar  at 

Temperature  of  room C.,        Tern,  of  jar  in  ice  C. 

First  observation    .     .     .  .cm.  cm. 

Second        "  .cm.  cm. 

Third  "  cm cm. 

etc.  etc.  etc. 

Mean •     cm.          cm. 

Wave  length     cm.         cm. 

Velocity  of  sound .     .     .      cm.          cm. 

Change  in  velocity  for  1°C cm. 

Vibration-number  of  tuning-fork  used  

435  Exercise.  —  Determine  the  velocity  of  sound  in 
carbonic  acid  gas. 

As  in  the  last  experiment,  obtain  the  air-column  giving  the 
loudest  reinforcement  of  the  tone  of  a  tuning-fork  whose  vibra- 
tion number  is  known.  Now  fill  the  jar  with  carbonic  acid, 
and  then  add  water  till  the  reinforcement  is  the  greatest. 
Proceed  as  in  the  last  experiment. 

Compare  the  ratio  of  the  velocity  of  sound  in  carbonic  acid 


SOUND.  247 

gas  and  in  air  with  that  of  the  densities  of  these  substances,  and 
determine  how  the  density  of  the  medium  affects  the  velocity  of 
sound.  Tabulate  results  as  in  the  last  experiment.  The  mo- 
ment when  the  cylinder  is  full  of  gas  can  be  determined  by 
inserting  a  burning  match ;  the  flame  will  be  extinguished  on 
reaching  the  gas. 

For  method  of  preparing  carbonic  acid  gas,  consult  Shepard's 
Chemistry,  Exp.  102. 

436.  Exercise.  —  Determine   the   velocity   of    sound    in 
hydrogen  or  coal  gas. 

Close  gas-tight  one  end  of  a  glass  tube  1  m.  long  and  4  cm. 
wide.  Fit  a  cork  into  the  other  end,  to  slide  with  slight  friction, 
using  a  long  stout  wire  for  a  piston-rod.  Mount  the  tube  in  a 
vertical  position,  mouth  downward,  with  the  piston  pushed  up 
to  the  closed  end.  Now  fill  the  tube  with  hydrogen  (see  Art. 
102),  by  displacement ;  and  then  by  moving  the  piston  deter- 
mine by  trial  the  position  where  the  loudest  resonance  is 
obtained  for  a  vibrating  tuning-fork  of  known  rate.  Then 
proceed  as  in  Art.  434.  What  does  this  experiment  show  is  the 
effect  of  density  on  the  velocity  of  sound  ? 

437.  Exercise.  —  Determine  the  ratio  of  the  velocity  of 
sound  in  a  rod  of  glass,  wood,  or  metal  to  that  in  air. 

Close  one  end  of  a  glass  tube  1  m.  long  and  4  cm.  wide  with 

a  cork,  A  (Fig.  181).  To  a  rod  1.5  m.  long  of  the  material  in 
which  the  velocity  of 

sound  is  to  be  deter-  /-*  c             B 

mined,  as  EB,  glue  a  E«              =y^-J^.           j| 

thin  cork  piston,  B,  of  f        ^/                            A    b 

such  a  size  as  to  slide  ^ — ^ — ^ 

r  IG*   lol* 

freely  within  the  tube 


248  PEACTICAL    PHY  SIC  ft. 

AC.  By  means  of  an  iron  clamp  fasten  the  rod  at  its  middle 
to  the  table,  between  two  pieces  of  wood,  having  the  shape 
shown  at  F  ;  the  thickness  being  such  that  the  rod  is  in  the  axis 
of  the  glass  tube  AC  as  it  rests  on  the  table  ;  the  hole  through 
these  pieces  being  just  large  enough  to  hold  the  tube  without 
crushing.  As  AC  is  free  either  to  move  toward  D  or  away 
from  it,  the  space  AB  can  be  lengthened  or  shortened  at  pleas- 
ure. Distribute  a  little  cork  or  silica  powder  evenly  between 
A  and  B.  Now  excite  longitudinal  vibrations  in  BE  by  gently 
stroking  it  toward  E  with  a  damp  cloth,  if  the  rod  is  glass, 
or  with  soft  leather  covered  with  powdered  rosin,  if  it  is 
wood  or  metal,  being  careful  not  to  spring  the  rod  out  of  line 
for  fear  of  breaking  it.  These  vibrations  will  be  communi- 
cated by  the  piston  B  to  the  air  between  A  and  B,  and 
disturb  the  powder.  By  moving  AC,  a  position  for  B  can  be 
readily  found  at  which  the  agitation  of  the  powder  is  greatest, 
being  thrown  into  clearly  marked  heaps  of  uniform  length  sub- 
divided into  parallel  ridges.  Find  the  average  length  of  these 
dust  heaps,  a&,  by  dividing  the  distance  between  A  and  B  by 
the  number  of  heaps.  Representing  this  length  by  s,  2  s  will 
be  the  length  of  the  air- wave.  If  the  length  of  the  rod  is  cf, 
since  it  is  clamped  at  the  centre,  then  2  d  is  the  wave-length  of 
the  vibration  produced  in  it.  Hence  d-^-s  represents  the  number 
of  times  that  sound  travels  faster  in  the  rod  than  in  air  at  the 
temperature  of  the  room.  Represent  by  V  the  velocity  of 
sound  at  the  temperature  of  the  room,  t.  Then  V  =  333 

(1  +  .0037  t)  *,  and  the  velocity  of  sound  in  the  rod  =  —  V. 


SOUND. 


249 


V.    PROPAGATION    OF    SOUND. 

438.  Apparatus.  —  Cardboard,   "Whirling-Machine,  etc. 

439.  Exercise.  —  Cut  out  of  stiff  cardboard  a  disk  hav- 
ing a  diameter  of  30  cm.     Concentric  with  the  circumference  of 
the  disk  draw  a  cir- 
cle with  a  radius  of 

2.5  mm.  Divide  the 
circumference  of  this 
small  circle  into 
twelve  equal  parts 
(Fig.  182),  number- 
ing them  1,  2,  3,  etc. 
With  the  point  1  as 
a  centre,  and  with 
a  radius  of  7  cm., 
draw  a  circle.  With 
2  as  a  centre,  and 
with  a  radius  of  7.3 
cm.,  draw  a  second  FlG- 182- 

one.  With  3  as  a  centre,  and  with  a  radius  of  7.6  cm.,  draw 
a  third  one.  Continue  in  this  way,  increasing  the  radius  each 
time  by  3  mm.,  till  each  point  has  been  used  twice  as  a  centre. 
The  lines  should  be  drawn  with  jet-black  ink,  and  should  be 
J  mm.  in  width.  Clamp  this  disk  on  the  spindle  of  the  whirl- 
ing-machine, and  hold  in  front  of  it,  and  as  close  as  possible, 
a  strip  of  cardboard  in  which  is  cut  a  slit  3  mm.  wide  and  10 
cm.  long.  In  this  opening  will  now  be  seen  parts  of  these 
circles  appearing  as  black  dots  unevenly  distributed.  Now 
rotate  the  disk  slowly,  and  waves  of  condensation,  followed 
by  waves  of  rarefaction,  will  appear  to  move  along  the  slit. 


250  PRACTICAL    PHYSICS. 

Watch  closely  one  dot,  and  from  its  motion  account  for  the 
effects  produced.  If  these  dots  represent  the  air-particles 
along  the  radius  of  a  series  of  sound  waves  set  up  in  air,  then 
in  their  motion  you  have  a  representation  of  the  movements  of 
the  air-particles  in  the  propagation  of  sound  waves. 

VI.    REFLECTION    OF    SOUND. 

440.  Apparatus.  —  Cardboard,  Whirling-Machine,  Watch, 
Concave  Reflector,  Tin  Tubes,  etc. 

441.  Exercise.  —  Cut  out  of  cardboard  a  disk  having  a 
diameter  of  30  cm.     Out  of  opposite  sides  of  the  disk  (Fig. 

183)  cut  two  sectors  of 
about  ten  degrees.  Clamp 
the  disk  to  the  spindle  of  a 
whirling-machine,  and  as  the 
disk  is  made  to  revolve,  blow 
a  whistle  or  toy  trumpet  in 
front  of  it,  and  close  to  it. 
Compare  the  sound  with  that 
when  the  disk  is  at  rest. 
When  is  the  sound  loudest? 
When  lowest?  Explain. 

FIG.  183. 

442.  Exercise.  —  Suspend   a    loud-ticking  watch   at  the 
focus  of  a  large  concave  reflector,  such  as  is  used  behind  wall 
lamps.     About  two  metres  from  this  place  a  second  reflector, 
parallel  to  the  first,  and  with  its  concave  surface  toward  the 
watch.     At  its   focus   support  a  small  funnel,  with  its  mouth 
toward  the  reflector,  and  a  rubber  tube  leading  from  its  stem  to 
your  ear.     Compare  the  distinctness  with  which  you  hear  the 


SOUND.  251 

ticking  of  the  watch  with  that  when  the  reflectors  are  removed. 
Explain. 

The  focus  of  the  reflector  can  be  found  by  letting  sunlight 
fall  upon  it,  and  marking  the  point  in  front  of  it  at  which  it  will 
set  fire  to  a  match. 

By  suspending  the  watch  a  few  centimetres  farther  away 
from  the  reflector  than  the  focus,  a  point  can  be  found  by  trial, 
still  farther  removed  from  the  reflector,  at  which  the  watch  can 
be  heard  with  much  greater  distinctness  than  at  any  intervening 
or  more  distant  points. 

443,  Exercise.  —  Determine  the  law  of  reflection  of  sound. 
Lay  on  a  table  two  tin  tubes,  each  1.5  m.  long  and  10  cm.  wide, 


FIG.  184. 

forming  a  V  (Fig.  184).  Suspend  a  loud-ticking  watch  in  the 
outer  end  of  one  of  the  tubes,  and  listen  for  the  sound  at  the 
outer  end  of  the  second  tube.  On  a  sheet  of  cardboard  draw  a 
semicircular  protractor  of  at  least  30  cm.  radius,  dividing  it 
into  10  sectors.  Let  these  tubes  rest  on  radial  lines,  on  oppo- 
site sides  of  the  zero,  so  that  the  angle  each  tube  makes  with 
the  zero  radius  can  be  read  off  on  the  scale.  Across  the  other 
ends  of  the  tubes,  and  perpendicular  to  the  zero  radius,  hold  a 
piece  of  cardboard.  Move  the  tube  to  which  the  ear  is  ap- 


252 


PRACTICAL    PHYSICS. 


plied  to  a  position  where  the  ticking  of  the  watch  is  most  dis- 
tinct. Compare  the  angles  between  the  zero  radius  and  the 
tubes.  Make  several  trials  for  different  positions  of  the  tubes. 
Tabulate  the  results.  Inference. 

VII.    REFRACTION    OF    SOUND. 

444.  Apparatus.  —  Rubber  Balloon,   Watch,   etc. 

445,  Exercise.  —  Fill  a  small  rubber  toy  balloon  with  car- 
bonic acid  by  tying  it  over  the  delivery-tube  of  a  carbonic  acid 
generator.     Suspend  a  loud-ticking  watch  from  a  suitable  sup- 


FIG.  185. 

port,  and  move  as  far  away  as  possible  and  still  hear  the  watch 
when  one  ear  is  turned  toward  it.  Now  hold  the  balloon  close 
to  the  ear,  and  ascertain  if  the  loudness  of  the  sound  is 
affected.  Explain. 

Fig.  185  illustrates  another  method  of  conducting  this  experi- 
ment. The  ear  is  placed  at/. 

446.  Exercise.  —  Fill  a  balloon  with  hydrogen  gas,  and 
proceed -as  in  the  last  experiment.  Explain.  Try  a  balloon 
filled  with  air.  Is  the  effect  the  same-? 


SOUND.  253 


VIII.       LOUDNESS    OF    SOUND. 

447.  Apparatus.  —  Tuning-Fork,     Sonometer,     Bell,     Air- 
Pump,   Tin  Tube,  Steel  Rod,  Glass   Tubes,   Fruit- Jar,   etc. 

448.  Exercise.  —  Compare  the  vibratory  movement  of   a 
feebly  sounding  tuning-fork  with  that  of  a  loud  sounding  one, 
by  means  of  the  effects  seen  on  touching  one  prong  to  the  sur- 
face of  water.     What  is  here  shown  to  be  the  cause  of  the 
difference  in  loudness? 

449.  Exercise.  —  Compare  the  vibratory  movement  of  a 
feebly  sounding  string  on  a  violin  or  sonometer  with  that  of  the 
same  string  when  loudly  sounding,  by  suspending  in  contact  with 
it  a  small  paraffine   ball.     Account  for  the  difference  in  loud- 
ness. 

450.  Exercise.  —  Ascertain  if   the    loudness  of  sound  is 
affected  by  the  density  of  the  medium  enveloping  the  vibrat- 
ing body. 

1st.    Observe  the  change  in  the  sound  emitted  by  a  small  bell 
under  a  bell- jar  of  an  air-pump,  as  the  rarefaction 
is  increased.     Inference. 

The  bell  should  stand  on  a  bed  of  cotton- wool. 
Why?  The  bell-jar  should  be  provided  with  a 
sliding-rod  for  ringing  the  bell  (Fig.  186). 

2d.  Fill  a  large  bell-jar  with  hydrogen,  by  dis- 
placement over  water.  With  one  hand  lift  the  jar 
vertically  upward,  and  with  the  other  ring  a  small 
bell  within  it.  Compare  the  sound  with  that  when 
the  jar  is  full  of  air.  Inference. 

Invert  the  jar,  fill  it  with  carbonic  acid  gas,  and  repeat  the 
test.     Inference. 


254  PRACTICAL    PHYSICS. 

451.  Exercise.  —  Lay  on  a  table  the  tin  tube  of  Art.  417. 
Hang  a  watch  in  the  opening  at  the  large  end,  place  your  ear 
at  the  other  end,  and  compare  the  loudness  of  the  ticking  with 
that  when  the  tube  is  removed.    Explain  the  action  of  the  tube. 

452.  Exercise.  —  Set  a  timing-fork  in  vibration,  and  com- 
pare the  sound,  when  held  in  the  hand,  with  that  when  its  stem 
is  held  firmly  in  contact  with  the  bottom  of  an  empty  chalk- 
box.     Ascertain  what  is  the  condition  of    the    box  when  the 
sounding  fork  is  in  contact  with  it,  by  noticing  the  effect  on  a 
little   fine  sand  sprinkled  over  it.     To   what  is   the  increased 
loudness  due? 

Find  out  whether  the  fork  vibrates  as  long  when  its  stem 
rests  against  the  box  as  when  held  in  the  hand.  In  making 
this  comparison,  blows  of  equal  intensity  must  be  given  to  the 
fork.  A  simple  method  of  doing  this  would  be  to  let  a  wooden 
ball  swing  against  the  prong,  falling  in  each  case  from  the 
same  height. 

If  you  have  two  forks  of  the  same  pitch,  remove  them  from 
the  sounding-boxes,  placing  the  boxes  on  the  table  in  front  of 
you.  To  give  both  forks  the  same  impulse,  cut  out  of  a  board 
about  6  or  8  mm.  in  thickness  a  piece  of  the  shape  shown 
in  Fig.  187,  the  width  of  each  of  the  prongs, 
A.  A,  being  somewhat  greater  than  the 
normal  distance  between  the  prongs  of  the 
tuning-fork.  Slip  the  latter  on  obliquely, 
and  straighten  up  at  right  angles  to  the  plane 
of  the  board,  with  the  surface  of  the  latter 
even  with  the  surface  of  the  ends  of  the 
prongs.  Arrange  the  other  fork  in  the  same 
manner,  with  respect  to  the  other  prong  of  the 
board.  Now  let  an  assistant  hold  the  handle 
of  the  board  and  strike  it  a  sharp  blow  with 


SOUND.  255 

a  hammer,  at  a  point  near  the  forks,  while  you  hold  the  latter, 
one  in  each  hand,  prongs  downward.  Both  forks  will  then  be 
put  in  vibration  with  nearly  the  same  amplitude.  Place  one 
on  its  sounding-box  immediately,  holding  the  other  in  the  hand. 
As  soon  as  the  sound  of  the  one  on  the  box  ceases  to  be  heard, 
place  the  one  held  in  the  hand  on  its  box.  Repeat  the  experi- 
ment, reversing  the  positions  of  the  forks,  to  determine  if  the 
difference  is  due  to  the  forks.  Why  does  the  energy  of  one 
fork  hold  out  longer  than  the  other  ? 

453.  Exercise.  —  Compare    the   loudness   of    the   sound 
emitted  by  a  vibrating  steel  rod,  clamped  by  one  end  in  a  vise, 
with  that   produced  by  a  steel  bar  of   the    same   length   and 
thickness,  but   having   considerable    width.     Account   for  the 
difference.     Compare   the   duration   of   the   sounds.     Why   is 
there  a  difference  ? 

Why  is  a  tuning-fork  usually  made  with  two  branches? 

454.  Exercise.  —  Procure   four  glass   tubes,  each   about 
30  cm.  long,  having  different  diameters,  as  1.5,  2.5,  3.5,  and 
4.5  cm.,  respectively.     Clamp  each  one  successively  in  a  verti- 
cal position,  with  one  end  dipping  into  a  vessel  of  water.     Hold 
over  the  open  end  a  sounding  tuning-fork,  raising  or  lowering 
the  tube  till  a  position  is  reached  where  the  sound  bursts  out 
with   maximum  loudness.     Measure   the    air-column   in   each 
case,  compare  it  with  that  given  by  computation  for  the  fork 
employed,  and  deduce  the  correction  to  be  made  for  the  diame- 
ter.    Tabulate  the  results. 

455.  Exercise.  —  Paste  a  piece  of  paper  over  the  mouth  of 
an  empty  glass  fruit- jar.     Cut  away  the  paper  cover,  little  by 
little,  the  part  removed  having  the  form  of  a  segment,  till  a 


256  PRACTICAL    PHYSICS. 

loud  resonance  is  obtained  on  holding  a  vibrating  tuning-fork 
close  to  the  opening.  Ascertain  the  cause  of  the  resonance  by 
sprinkling  a  little  fine  sand  over  the  paper,  and  watching  it  as 
the  sounding-fork  approaches  the  opening. 

456.  Exercise.  —  Compute  the  length  of  the  air-column  2 
cm.  in  diameter  that  will  reenforce  a  fork,  say  C ',  at  the  tempera- 
ture of  the  room.     Then  cut  eight  glass  tubes  of  this  length  and 
diameter  (see  page  354) ,  grinding  the  ends  smooth  on  a  piece  of 
sandstone  wet  with  spirits  of  turpentine.      Cut  a  number  of 
paper  disks,  of  the  same  diameter  as  the  outside  of  these  tubes, 
and  also  a  number  of  rubber  connectors.     Now  it  is  evident 
that  a  tube  whose  length  is  any  multiple  of  the  first  can  be  pre- 
pared by  joining  these  together  with  the  rubber  connectors,  and 
that  by  cementing  a  paper  disk  over  the  end  of  a  tube  an  open 
one  can  be  changed  into  one  closed  at  one  end. 

Prepare  open  tubes  whose  lengths  are  respectively  2,  3,  4, 
etc.,  times  the  length  of  the  first,  and  determine  by  trial  which 
reenforces  the  sound  of  the  fork  used  in  preparing  the  tubes. 

Prepare  and  test  closed  tubes  in  the  same  way. 

If  we  represent  by  one  the  length  of  the  shortest  open  tube 
which  reenforces  the  sound,  what  will  be  the  lengths  of  the 
different  open  tubes  found  to  reenforce  it? 

Prepare  a  similar  series  for  closed  tubes. 

IX.      INTERFERENCE    OF    SOUND. 

457.  Exercise.  —  Tuning-Fork,   Sonometer,  T-tubes,    Rub- 
ber Tubing,  Glass  Tubing,   etc. 

458.  Exercise.  —  Hold  a  vibrating  tuning-fork  near  the 
ear,  and  as  you  rotate  it  slowly  about  the  axis  of  the  stem, 


SOUND.  257 

mark  the  positions  where  the  sound  is  feeblest,  and  also  those 
where  loudest.  Now  hold  the  same  fork  over  a  cylindrical  jar, 
serving  as  a  resonator ;  find  by  trial  the  position  in  which  the 
sound  is  feeblest ;  then  cut  off  the  waves  sent  out  by  one  prong, 
by  sliding  over  it  a  paper  cylinder,  without  touching  it,  and  ob- 
serve the  effect.  Explain  the  varying  loudness  of  the  sound  as 
the  fork  rotates  about  the  axis  of  the  stem. 

459.  Exercise.  —  Mount  on   resonant  boxes   two   large 
tuning-forks  of  the  same  pitch  (Fig.  188).    Stick  a  piece  of  seal- 
ing-wax, the  size  of  a  hickory  nut,  on  the  end  of 
one  branch  of  one  of  the  forks.     Set  the  forks 
in  vibration,  and  compare  the  sound  with  that 
emitted    by   them    before   they   were   loaded. 
Ascertain    the    effect   of    using   a   lighter   or 
heavier  load.     Explain. 

A  resonant  box  is  a  rectangular 
box  of  pine,  open  at  one  end.  Its 
length  is  one-fourth  of  a  wave-length 
of  the  fork,  less  about  two-fifths  of 
the  diagonal  of  the  end  of  the  box. 

460.  Exercise.  —  Tune  two  strings  on  the  sonometer  to 
the  same  pitch,  and  then  compare  the  sound  emitted  by  them 
when  plucked  simultaneously    with   that  when  the  tension   of 
one  string  has  been  slightly  changed. 

461.  Exercise.  —  Connect  two  large  T-tubes  with  rubber 
tubing,  as  shown  in  Fig.  189.     Join  a  funnel  to  the  stem  of  one 
of  them,  and  a  piece  of  rubber  tubing  to  the   other.     Hold  a 
vibrating  tuning-fork  at  A.     Now  it  is  evident  that  the  waves 
divide  at  B,  part  traversing  each  branch,  and  unite  again  at  K, 


258 


PRACTICAL    PHYSICS. 


reaching  the  ear  through  H.  If  the  tube  CDE  is  half  a  wave- 
length longer  than  F,  the  waves  will  meet  in  opposite  phases  at 
K,  and  no  sound  at  H  will  be  heard.  Similar  effects  will  fol- 
low if  the  difference  is  f ,  f ,  f ,  etc.,  of  a  wave-length.  If  CDP] 
is  a  wave-length  or  some  multiple  of  a  wave-length  longer,  no 
diminution  of  intensity  will  be  noticed.  Any  differences  in 
length  other  than  these  will  result  in  partial  interference. 


FIG.  189. 

Friction  of  the  waves  on  the  walls  of  the  tubing  will  produce 
slight  deviations  from  the  above  results,  and  the  sound  may  not 
be  completely  extinguished  owing  to  the  conductivity  of  the 
material. 

462.  Exercise.  —  Set  up  two  singing  flames  (see  Art.  426) , 
employing  tubes  of  the  same  length  and  diameter.     Make  a 
paper  cylinder  to  slide  with  a  little  friction  over  the  end  of  one 
of   the  tubes  so  that  its  length  may  be  increased  if  desired. 
Adjust  the  lengths  of  the  tubes  by  moving  the  paper  cylinder 
till  the  tones  are  alike ;  then  note  the  effect  of  changing  the 
position  of  the  paper  cylinder. 

X.    SYMPATHETIC  VIBRATIONS. 

463.  Apparatus.  —  Pendulums,     Bar     Magnets,     Tuning- 
Forks,  Glass  Tubing,  Sonometer,   etc. 

464.  Exercise.  —  Suspend  a  heavy  weight  by  a  wire  or 
string  1  m.  long,  and  find  the  time  of  vibration.     Now  try  to 


SOUND.  259 

put  this  pendulum  in  vibration  by  puffs  of  air  directed  against 
the  centre  of  the  weight,  and  timed  in  unison  with  the  pendu- 
lum. Try  puffs  of  air  irregularly  timed.  Try  puffs  of  air 
whose  period  is  some  multiple  of  that  of  the  pendulum. 

Arrange  a  second  pendulum  to  swing  in  the  same  time  as  the 
first.  Connect  the  bobs  of  the  two  pendulums  by  a  string, 
which  is  drawn  straight  when  the  pendulums  hang  vertically. 
Now  set  one  of  the  pendulums  in  vibration,  in  the  plane  of  the 
two,  and  note  the  effect  on  the  second  one.  Shorten  one  of  the 
pendulums  by  lowering  the  suspension-point,  keeping  the  bobs 
in  the  same  horizontal  line,  and  ascertain  if  the  effect  is  the 
same  as  before.  Substitute  a  stiff,  very  light  bar  for  the  string 
between  the  bobs,  and  observe  the  effect  on  the  time  of  vibra- 
tion. 

465.  Exercise.  —  Suspend  two  pendulums,  each  one  metre 
long,  from  a  horizontal  bar ;  a  third,  one-fourth  of  a  metre 
long ;  a  fourth,  one-half  of  a  metre  long ;  a  fifth,  90  cm.  long. 
Set  one  of  the  first  two  in  vibration,  and  observe  the  effect  on 
the  others.     Explain. 

466.  Exercise.  —  Construct   two    pendulums,   using    bar 
magnets   for   bobs.      Suspend   each  magnet  by   two   threads, 
each  50  cm.   long,   so  that  it  hangs  horizontally.     Place  the 
magnets   parallel,    unlike   poles    adjacent    and    several   centi- 
metres apart.     Now  set  one  pendulum  in  vibration  in  a  plane 
perpendicular  to  the  other  magnet,  and  study  the  motions  for 
some  time.     Explain.     Shorten  one  of  the  pendulums,  by  low- 
ering its  supporting-point,  without  changing  the  position  of  the 
magnet,  and  ascertain  if  the  effects  are  the  same  as  before. 

467.  Exercise.  —  Place  near  each  other  on  the  table  the 
tuning-forks  of  Art.  459.     Set  one  of  them  in  vibration,  and 


260  PRACTICAL    PHYSICS. 

after  waiting  a  few  minutes  stop  it  and  listen  near  the  other  one 
to  ascertain  whether  it  is  motionless  or  not.  Would  the  effect 
be  the  same  if  one  of  the  forks  were  surrounded  witli  a  paper 
cylinder  ?  What  would  be  the  effect  of  changing  the  pitch  of 
one  fork  by  sticking  a  piece  of  sealing-wax  to  one  of  its  prongs  ? 
AVhy? 

468.  Exercise.  —  Tune  in  unison  two  strings  on  a  sonome- 
ter  (Fig.  192),  or  a  violin.     Set  one   string  in  vibration  ;  then 
after  a  few  moments  dampen  it  with  the  hand,  and  ascertain  if 
the  second  one  is  silent.     Shorten   one  string  by  moving  the 
bridge  under  it  and  repeat  the  experiment.     Explain. 

469.  Exercise. — Prepare  a  singing-flame  as  in  Art.  426. 
Now  shift  the  position  of  the  jet  within  the  tube  by  lowering  it 
just  enough  to  stop  its  singing,  and  then  sound  near  it  the  same 
note  as  was  emitted  by  the  tube  at  first.     Can  you  account  for 
the  effect  on  the  flame?     Will  singing  a  higher  or  lower  tone 
work  as  well  ?     Try  it. 

470.  Exercise.  —  Prepare  a  jet-tube  by  holding  one  end  of 
a  piece  of  glass  tubing  in  a  gas- flame  till  the  opening  has  been 
reduced  to  about  1  mm.  wide.     Connect  this  by  a  rubber  tube 
to  the  gr.s- supply,  and  regulate  the  flow  till  a  flame  some  30  cm. 
or  more  in  length  is  obtained,  and  just  on  the  point  of  flaring. 
Now  blow  a  shrill  whistle,  rattle  a  bunch  of  keys,  or  hiss,  and 
the  long  flame  will  be  shortened  nearly  half,  and  rustle  loudly. 
Turn   your   back   toward    the   flame  and   repeat   the    sounds. 
Repeat  the  experiment,  standing  in  a  distant  part  of  the  room. 
Explain. 

If  the  gas- pressure  is  not  sufficient  to  give  a  flame  of  the 
character  described,  fill  a  large  rubber  bag  with  gas,  connect 


SOUND. 


261 


the  jet-tube  to  it,  and  apply  pressure  to  the  bag  by  means  of  a 
heavy  weight. 

XI.      PITCH    OF    SOUND. 

471.  Apparatus.  —  Siren,  Cylindrical  Jar,  Tuning-Forks,  etc. 

472.  Exercise.  —  Measure  the  number  of  vibrations  made 
in  a  second  by  a  vibrating  body. 

First  Method.  — Cut  out  of  cardboard  a  disk  25  cm.  in  di- 
ameter. Draw  on  it  four  concentric  circumferences,  having  the 
diameters  23,  21.5,  20,  and 
18:5  cm.  respectively  (Fig. 
190).  Divide  these  circum- 
ferences into  48,  36,  30,  and 
24  equal  parts  respectively.  At 
these  points  of  division,  with  a 
sharp,  hollow  punch,  having  a 
diameter  of  about  1  cm.,  cut 
round  holes.  Mount  this  disk 
on  the  spindle  of  a  whirling- 
machine,  or  on  the  armature- 
shaft  of  a  small  electric  motor, 
and  you  have  a  form  of  Siren. 

If,  with  a  rubber  tube,  you  direct  a  steady  stream  of  air 
against  one  of  these  rows  of  holes  as  the  disk  rotates  rapidly, 
a  musical  note  is  produced  by  the  air-puffs  passing  through 
them.  Find  what  the  pitch  of  the  tone  depends  upon. 

Now  give  the  disk  such  a  speed  that  the  tone  emitted  by 
blowing  steadily  against  one  of  the  circular  rows  of  holes  is  in 
unison  with  that  produced  by  the  body  in  question.  Count 
the  number  of  revolutions  made  by  the  drive-wheel  in,  say,  20 
seconds,  the  speed  being  kept  constant.  Find  the  relative 
size  of  the  drive-wheel  and  the  spindle -pulley,  and  from  the 


FIG.  190. 


262 


PRACTICAL    PHYSICS. 


data   compute  the   number  of   revolutions  made  by  the   disk 
in  a  second.     This  multiplied  by  the  number  of  holes  in   the 

circle  will  give  the  vibration-number 
sought. 

The  speed  of  the  armature  of  the 
electric  motor  may  be  determined  by 
clamping  in  contact  with  it  a  speed- 
indicator,  such  as  machinists  use  in 
ascertaining  the  speed  of  shafting. 

In  Fig.  191  is  shown  a  form  of 
siren  with  a  counter.  The  perforated 
disk  is  given  a  horizontal  position, 
and  made  to  rotate  by  the  stream  of 
air  forced  through  the  obliquely  cut 
openings  by  means  of  a  bellows. 

Second     Method.  —  Compute     the 
velocity  of  sound  in   metres   by   the 
formula    v  =  333    (1  +  .0037  £)*   in 
which  t  is  the  temperature  of  the  room 
in  centigrade  degrees.     Now  find  by 
trial  the  length  of    the   shortest  air- 
column  giving  the  loudest  resonance  when  the  sounding  body 
is  held  over  it,  correcting   it    for   the    diameter  of   the    tube. 

Then  n  =  ~—  in  which  I  is  the  wave-length  as   given    by  the 
air-column. 


473.  Exercise.  —  Determine  the  difference  of  rate  of  vibra- 
tion of  two  sounding  bodies,  not  quite  in  unison,  by  counting  the 
number  of  beats  produced  during  some  convenient  unit  of  time, 
as  30  seconds,  and  then  computing  the  number  per  second. 


SOUND.  263 


XII.    T.AWS    OF    VIBRATING    RODS    AND    STRINGS. 

474.  Apparatus.  —  "Wooden  Rod,  Sonometer,  Siren,  Tuning- 
Forks,  etc. 

475.  Exercise.  —  Determine  the  laws  governing  vibrating 
rods. 

Take  a  pine  strip  2  m.  long,  3  cm.  wide,  and  6  mm.  thick,  a 
second  one  of  the  same  length  and  width,  but  12mm.  thick,  and 
a  third  one  of  the  same  length  and  thickness,  but  6  cm.  wide. 
Clamp  these  at  one  end  over  the  edge  of  a  table  with  small  iron 
clamps,  set  each  in  vibration,  in  succession,  and  count  the  number 
of  vibrations  made  in  some  convenient  period  of  time.  What 
effect  does  width  and  thickness  have  on  the  vibration-rate? 
Now  clamp  the  first  one  at  the  middle  so  that  one-half  of  it  is 
free  to  vibrate,  and  determine  its  rate.  What  effect  does  length 
have  on  the  vibration-rate  ? 

Express  as  laws  the  results  of  these  experiments. 

476.  Exercise.  —  Determine  the  laws  governing  vibrating 
strings. 

A  Sonometer  (Fig.  192)  and  a  Siren  (Fig.  190)  will  be  re- 
quired for  this  experiment.  The  former  is  a  wooden  box  about 
150  cm.  long,  15  cm.  wide,  and  10  cm.  deep.  The  material  is 
pine,  free  from  pitch,  straight-grained,  and  about  1  cm.  thick, 
except  the  top,  which  may  be  5  mm.  thick  ;  the  ends  should  be  of 
hard  wood,  and  have  a  thickness  of  about  25  mm.  Near  the  ends 
glue  triangular  pieces  of  hard  wood,  to  serve  as  bridges  across 
which  to  stretch  the  wires.  The  depth  of  these  bridges  should 
be  about  2  cm.,  and  the  distance  between  them  120  cm.  ID 
one  of  the  head  pieces  insert  two  stout  pins,  and  in  the  other 
two  screws,  such  as  are  used  in  pianos,  for  changing  the 


264  PRACTICAL   PHYSICS. 

tension  of  the  wires.  In  the  same  end  screw  a  small  iron 
pulley  so  that  one  wire  may  be  drawn  over  it  and  the  tension 
measured  by  weights,  or  by  a  spring  balance.  Suitable  weights 
are  easily  made  out  of  sheet-lead,  riveting  a  number  of  thick- 
nesses together  till  the  required  thickness  is  obtained.  A  sliding 
weight,  on  a  lever,  having  its  fulcrum  at  the  end  of  the  box, 
might  be  substituted  for  the  pulley  and  weights.  Beneath  one 
of  the  wires  graduate  a  scale  to  half -centimetres. 

Now  stretch  a  piano-wire  or  a  catgut  string  on  the  sonometer, 
and  produce  with  the  siren,  using  the  inner  row  of  holes,  a 
tone  in  unison  with  that  given  by  this  string.  Without  -chang- 


FlG.  192. 

ing  the  speed  of  the  siren-disk  compare  the  tone  produced  on 
using  the  outer  circle  of  holes  with  that  given  by  the  string 
when  its  length  is  reduced  one-half  by  means  of  a  movable 
bridge  placed  beneath  the  middle  of  the  wire.  Also  compare  the 
tone  given  by  the  next  to  the  outer  row  of  holes  with  that  given 
by  the  string  when  its  length  is  but  two-thirds  of  the  whole. 
Also,  compare  the  tone  given  by  the  next  to  the  inner  row  of 
holes  with  that  given  by  the  string  when  its  length  is  imulr 
four-fifths  of  the  whole.  How  do  these  siren-tones  compare  in 
vibration-rate?  What  law  must  then  connect  pitch  and  length 
of  string  ? 


SOUND,  265 

Stretch  two  piano-wires  or  catgut  strings  of  the  same  diam- 
eter on  the  sonometer,  one  of  them  in  such  a  way  that  the  ten- 
sion can  be  measured.  Adjust  the  tension  till  the  strings 
sound  in  unison  ;  there  will  then  be  no  audible  beats.  Now, 
increase  the  tension  of  one  of  the  wires  till  it  is  in  unison  with 
the  other  one,  reduced  in  length  one-half  by  means  of  the 
movable  bridge.  How  have  you  affected  the  vibration- rate  in 
reducing  the  length  one-half  ?  What  effect  must  tension  have 
on  the  rate? 

Stretch  two  wires  or  strings  on  the  sonometer,  the  ratio  of 
their  weights  being  1  :  4.  Steel  wires  No.  27  and  21  B.  W.  G., 
or  No.  24  and  19,  will  very  nearly  fulfil  this  condition  (see 
Appendix  C).  Note  the  tension  on  the  heavy  string  when  its 
tone  is  of  the  same  pitch  as  given  by  the  lighter  one.  Without 
changing  the  tension  in  either  case  substitute  for  the  heavy  one 
a  wire  exactly  like  the  small  one.  Place  a  bridge  under  the 
first  wire  at  a  point  where  it  will  cause  it  to  vibrate  in  unison 
with  the  second  one.  What  must  have  been  the  difference  of 
pitch  of  the  first  two  wires  ?  What  effect  must  weight  have  on 
pitch  ? 

Stretch  with  equal  tensions  a  steel  and  a  brass  wire  of  the 
same  gauge-number.  Compare  the  pitch  of  the  sounds.  By 
means  of  the  movable  bridge  determine  the  difference  in  pitch, 
and  hence  the  ratio  of  the  densities  of  the  two  substances. 

What  three  laws  for  vibrating  strings  do  you  derive  from  the 
above  experiments  ? 

477.  Exercise.  —  Set  a  large  tuning-fork  firmly  in  a  block 
of  wood,  and  clamp  it  to  the  table.  Tie  a  metre  of  tine  thread 
to  the  end  of  one  of  its  prongs,  pass  this  thread  through  a 
small  ring  held  in  a  clamp,  and  to  the  free  end  attach  a  small 
paper  tray  of  known  weight.  The  thread  and  the  prongs  of 


266  PRACTICAL   PHYSICS. 

the  fork  must  lie  in  the  same  plane  and  the  thread  should 
have  a  horizontal  position.  Now  put  known  weights  into 
the  tray  till  such  a  tension  is  secured  that,  on  setting  the 
fork  in  vibration,  the  thread  will  also  be  thrown  into  vibration, 
swinging  in  one  segment.  Without  changing  the  length  of  the 
thread  make  the  tension  one-fourth  of  what  it  was  at  first, 
and  record  the  number  of  segments  in  which  the  thread  vibrates. 
Try  a  tension  one-ninth  of  the  first.  What  relation  is  shown 
by  these  results  to  exist  between  tension  and  vibration-rate  of 
strings  ? 

Ascertain  the  effect  on  the  length  of  string  required,  of 
lowering  the  pitch  of  the  fork,  by  sticking  a  heavy  coin  to  the 
free  end  of  one  of  its  prongs.  What  law  is  here  suggested  in 
regard  to  the  relation  existing  between  the  vibration-rate  and 
the  length  of  the  string? 

Substitute  for  the  single  thread,  one,  a  third  of  which  is  four 
of  these  threads  twisted  together,  and  the  remaining  part  is 
single.  Change  the  tension  till  the  string  divides  into  two 
segments,  and  observe  their  relative  lengths.  What  effect  does 
the  weight  of  the  string  have  on  the  vibration-rate  ? 

A  heavy  wire  stretched  on  the  sonometer  may  be  substituted 
for  the  fork.  The  thread  is  attached  to  the  centre  of  the  wire 
and  stretched  at  right  angles  to  the  wire.  The  sonometer  wire 
is  set  in  vibration  with  a  violoncello-bow. 


XIII,    OVERTONES. 

478.  Apparatus.  — Sonometer,  C'-Fork,  etc. 

479.  Exercise.  —  Tune  one  of  the  sonometer  strings  till  it 
vibrates  in  unison  with  a  C'-fork.     Place  the  movable  bridge  at 
the  middle  of  the  scale,  that  is,  at  60,  if  the  scale  is  120  cm. 


SOUND.  267 

long.  The  string  will  now  give  as  its  fundamental  the  first 
overtone  of  C'.  Place  the  bridge  successively  at  40,  30,  24, 
20,  17^,  15,  13£,  and  12.  The  shorter  part  of  the  string  in 
each  case  will  give  respectively  the  second,  third,  etc.,  over- 
tones of  C'.  Ascertain  the  names  of  these  tones  on  the  Dia- 
tonic Scale. 

480.  Exercise.  —  Pluck  the   sonometer  string  at  a  point 
other  than   its  centre,  and    immediately    touch  the  tip  of    the 
finger  to  the  middle  of  the  wire.     The  fundamental  tone  ceases, 
but  whence  the  sound  still  heard  ?     Compare  its  pitch  with  that 
of  the  sound  emitted  by  the  wire  with  the  bridge  at  the  middle. 
Ascertain  whether  the  same  tone  is  obtained  or  not  by  dampen- 
ing the  wire  at    the  middle,  after  setting    it   in  vibration    by 
plucking   it  at   the  middle.     Compare  the  quality  of  the  tone 
given  by  the  whole  wire  when  plucked  at  the  middle  with  that 
when  plucked  at  some  other  point.     Account  for  the  difference, 
basing   the    explanation   on    the    facts    revealed  by  the  above 
experiments.     How  can  any  overtone    be    eliminated  from  the 
sound  produced  by  a  vibrating  string? 

In  like  manner  search  for  other  overtones. 

481.  Exercise.  —  Tune    two    strings   in   unison    on    the 
sonometer.     Place  a  bridge  under  the  middle  of   one  of  them, 
and  place  on  the   same  wire  at  various  points  small  V~snaPed 
pieces  of  paper,  called  Eiders.     Now  pluck  the  whole  string  at 
its  middle  and  compare  the  effect  on  the  riders  with  that  when 
plucked  at  some  other  point.     Inference. 

Try  the  bridge  at  one-third  from  the  end,  one-fourth,  etc., 
and  ascertain  if  the  whole  string  vibrates  in  thirds  and  fourths 
when  plucked  at  a  point  intermediate  between  thirds  and 
fourths  of  the  string. 


268  PBACTICAL    PHYSICS. 

XIV.     LAWS    OF    SOUNDING    AIR-COLUMNS. 

482.  Apparatus.  —  Glass  Tubing,   Organ-Pipe,   etc. 

483.  Exercise. —  Prepare,  as  described  in  Art.  456,  eight 
glass  tubes,  with  paper  disks  and  rubber  connectors. 

1st.  Join  two  of  the  tubes  together  ;  close  one  end  and  find 
by  trial  a  tuning-fork  whose  tone  it  enforces.  Compare  the 
rate  of  this  fork  with  that  of  the  fork  used  in  preparing  the 
tubes.  Prepare  closed  tubes  that  will  enforce  the  tone  of  such 
other  forks  as  you  have.  What  do  you  find  that  the  pitch 
depends  upon? 

2d.  Prepare  open  tubes  that  will  enforce  the  sound  pro- 
duced by  the  forks  employed  in  the  first  case.  Compare  the 'ir 
lengths  with  those  of  the  corresponding  closed  tubes.  Formu- 
late a  law  expressing  these  results. 

3d.  Connect  two  closed  tubes  which  enforce  the  same  fork 
by  their  closed  ends,  and  select  a  fork  which  they  now  enforce. 
Remove  the  partitions,  and  see  whether  the  air-column  will  still 
enforce  the  same  fork  or  not.  What  does  this  show  to  be  the 
condition  of  the  air  at  the  middle  of  an  open  tube  which 
enforces  a  certain  sound? 

484.  Exercise.  — Fit  to  a  glass  tube,  2  cm.  wide  and  40 
cm.  long,    a  cork    piston.     Now  set  the  piston  so  that  the  air- 
column  reenforces  C'-fork.     Blow  gently  across  the  open  end 
of  the  tube,  and  compare  the  pitch  of  the  sound  with  that  of  the 
fork.     A  piece   of    rubber  tubing,  flattened  at  the  end  by  com- 
pressing it  between  the  thumb  and  finger,  may  be  used  for  the 
purpose  ;  or,  better  still,  a  piece  of  thin  brass  tubing  flattened  at 
the   end,  leaving  an  opening  1   mm.   in  width.     Measure    the 
length  of  the  column.     In  like  manner  find  the  lengths  for  D', 


SOUND.  269 

E',  etc.,  C".     Compare  the  ratios  of  these  lengths  with  those 
of  the  vibration-ratios,  and  write  the  law  suggested. 

485.  Exercise.  —  Ascertain  the  condition  of  the  air  in  a 
sounding  air-column. 

A  small  Organ-pipe,  made  either  of  glass,  or  having  one  glass 
side  (Fig.  193),  and  a  small  wire  ring  covered  with 
thin  paper,  will  be  needed.  Sift  a  little  sand  over 
the  paper  membrane  and  let  it  down  by  a  cord  into 
the  tube,  supported  vertically.  Blow  gently  through 
the  mouth-piece,  producing  the  fundamental  tone ; 
at  the  same  time  move  the  ring  up  and  down 
within  the  tube.  Nodes  will  be  known  by  the  sand 
remaining  almost  at  rest. 

Close  the  tube  with  a  cork  having  a  hole  through 
it  for  the  cord  supporting  the  ring,  and  again  search 
for  nodes. 

If  the  force  of  the  air-current  is  increased,  the 
pipe  will  give  an  overtone.  Again  search  for 
nodes. 

Make  a  cork  piston  and  slide  it  along  the  tube  till 
it  reaches  the  place  where  a  node  was  found,  and 
compare  the  sound  with  that  before  the  piston  was 
introduced.  Inference.  B^e.  193. 

486.  Exercise.  —  Employing  the  apparatus  of  Art.  456, 
connect  several  of  the  tubes  together,  close  one  end,  and  blow 
gently  across  the  open  end  to  produce  the  fundamental  (lowest) 
tone.1     Now  increase  the  force  of  the  blast  till  an  overtone  is 
produced  ;  that  is,  a  sound  of  higher  pitch.     Find  by  trial  what 


iThis  will  require  considerable  skill,  as  it  is  difficult  to  obtain  the  fundamental  tone 
of  a  tube  of  small  diameter  when  the  length  is  great  in  comparison. 


270  PRACTICAL    PHYSICS. 

length  of  closed  tube  has  for  its  fundamental  the  previously  ob- 
tained overtone.  Determine  from  the  number  of  tubes  used 
which  overtone  you  have.  In  like  manner  search  out  other 
overtones.  Repeat  the  experiment,  employing  open  tubes. 
What  overtones  are  found  to  accompany  closed  tubes  ?  Open 
tubes  ? 


XV.    HARMONY    AND  DISCORD. 

487.  Apparatus.  —  Tuning-Forks,  Sonometer,  etc. 

488.  Exercise.  —  Compare  the  pleasantness  of  the  sound 
produced  by  two  tuning-forks,  of  the  same  pitch,  with  that  when 
to  a  prong  of  one  of  them  is  cemented  a  small  coin.     First,  at- 
tach the  coin  near  the  stem ;  then  at  the  middle  of  one  branch ; 
and  finally  at  the  end.     Explain. 

If  you  have  the  forks,  compare  C'  and  D',  Cf  and  E',  C' 
and  F  ',  C  '  and  G  ',  C  '  and  A  ',  C '  and  B ',  C  '  and  C  ", 
etc.  Tabulate  those  which  are  found  to  harmonize. 

Adjustable  tuning-forks  are  now  to  be  had  of  dealers  in  mu- 
sical wares,  at  very  reasonable  prices.  With  two  such  forks 
all  these  comparisons  can  be  made. 

The  following  substitute  may  be  made  for  the  forks  :  Set  in 
holes,  bored  in  a  board,  thirteen  test-tubes,  each  15  cm.  long 
and  about  2  cm.  in  diameter.  Into  each  pour  melted  paraffine 
till  an  air-column  is  obtained  which  responds  to  some  one  of 
the  thirteen  notes  in  the  octave.  Now,  proceeding  as  in  Art. 
484,  any  one  of  these  may  be  sounded,  and  by  using  a  tube 
with  two  branches,  any  two  may  be  sounded  together. 

489.  Exercise.  —  Tune  two  strings  on  a  sonometer  to  the 
pitch  of  C'.      By  means  of  the  movable  bridge  under  one  of  the 


SOUND.  271 

strings  produce  successively  the  notes  of  the  musical  scale. 
Determine  which  harmonize  with  C ',  and  which  do  not.  Com- 
pare other  tones  by  placing  a  bridge  under  each  wire. 

As  placing  a  bridge  under  a  wire  will  increase  the  tension, 
where  both  ends  of  the  wire  are  connected  to  posts,  some 
allowance  will  have  to  be  made  for  this. 


XVI.     VIBRATING    PLATES    AND    BELLS. 

490.  Apparatus.  —  Chladni-Plates,  Large  Bell,  etc. 

491.  Exercise.  —  Cut  out  of  sheet-brass,  1  mm.  thick,  a 
plate  25  cm.  square, 

a  triangular  one,  25 

cm.    on   each  side, 

and  a  circular  one 

25  cm.  in  diameter. 

Mount  each  one  on 

a  support,  as  shown 

in  Fig.  194.    Round 

the    edges    with    a 

file.      Clamp    each 

stand  firmly  to  the  table,  sift  some  fine  sand 

evenly   over   the    plate ;    then,  touching  the 

plates  at  some  point  with  the  finger,  draw  a 

well-rosined  violin-bow  across  an  edge.    Try  touching  the  plate 

at  different  points.     Copy  in  your  note-book  the  figures  formed. 

Do   you    discover    any    relation   between   the   pitch   and  the 

figures  ? 

492.  Exercise.  —  Using  the  square  plate  of  the  last  ex- 
periment, make  it  vibrate  so  that  the  only  nodal  lines  are  diag- 


272 


PRACTICAL   PHYSICS. 


onals  of  the  square.  While  the  plate  is  vibrating,  hold  over 
opposite  segments  or  quarters,  and  close  to  the  plate,  stiff  pa- 
per triangles,  having  the  shape  and  size  of  these  segments. 
Observe  the  effect  on  the  loudness  of  the  sound.  Explain. 

493.  Exercise.  —  Pro- 
cure, of  a  tinsmith,  a  tube 
0  cm.  wide  and  40  cm.  long, 
having  two  branches  4  cm. 
wide,  20  cm.  long,  and  15 
cm.  apart  at  the  free  end 
(Fig.  195).  Hold  the  ap- 
paratus above  the  square 
plate  of  Art.  491,  with  the 
branches  within  1  cm.  of  its 
surface. 
Paste  a 
membrane 
of  thin  pa- 
per across  the  upper  end,  and  scatter  on  it  a 
little  fine  sand.  Cause  the  plate  to  vibrate  in 
quarters.  Compare  the  effect  on  the  sand  when 
the  arms  are  over  a  and  b  (Fig.  196)  with  that  when  over  a  and  c. 


FIG.  195. 


FIG.  196. 


494.  Exercise.  —  Invert  a  large  bell,  and  nearly  fill  it  with 
water.     Scatter  lycopodium  powder  or   cork-dust  on  the  sur- 
face.    Set  the  bell  in  vibration  by  a  blow  from  a  small  mallet. 
Determine  from  the  effect  on  the  powder  the  position  and  num- 
ber of  the  nodal  points.     A  large  glass  goblet  or  bell-jar  might 
be  substituted  for  the  bell. 

495.  Exercise.  —  Employing  the  bell  of  the  last  experiment, 
determine  the  position  and  the  number  of  the  nodal  points  by 


SOUND.  273 

means  of  a  small  glass  or  ivory  ball,  suspended  by  a  fine 
thread.  The  nodes  will  be  recognized  as  places  where  the  ball 
is  repelled  the  least  by  the  vibrating  surface. 


XVII.    ATTRACTION    OF    VIBRATING    BODIES. 

496.  Apparatus. — -Tuning-Fork,  Rubber  Balloon,  etc. 

497.  Exercise.  —  Float   an  inflated   rubber  balloon   on  a 
vessel  of  water,  shielding  it  carefully  from  air-currents.     Hold 
near  the  balloon  a  large,  vibrating  tuning-fork,  and  observe  the 
action  of  the  ball.     Repeat  several    times  to  make  it  certain 
that  the  effect  observed  is  not  accidental.     What  must  be  the 
atmospheric   condition    about   the  fork   to   produce   the  effect 
noticed  ? 

498.  Exercise.  —  Sprinkle  evenly  over  the  square  plate  of 
Art.  491   a   mixture    of    fine    sand    and   lycopodium    powder. 
Cause  the  plate  to  vibrate,  and  compare  the  effects  produced 
on  the  powder  and  sand  respectively.     Explain. 


XVIII.     GRAPHIC    AND    OPTICAL    STUDY    OF    SOUND. 

499.  Apparatus.  —  Tuning-Forks,     Glass     Plates,     Vibro- 
graph,  Logograph,  Manometric  Flame   Apparatus,   Lissajou  Ap- 
paratus, Sand   Pendulum,    etc. 

500.  Exercise.  —  Cut  a  wooden  block  of  the  form  shown 
in  Fig.  197,  in  which  is  firmly  set  the  stem  of  a  tuning-fork. 
Make  out  of  thin  brass  a  narrow  rectangular  ferrule,  with  a 


274 


PRACTICAL  PHYSICS. 


FIG.  197. 


short  pointed  arm  projecting,  to  slip  over  the  end  of  one  branch 

of  the  fork  to  serve  as  a  marker. 
Beneath  the  point  support  a  pane  of 
glass  sufficiently  inclined  to  cause  a 
small  plate  of  glass  placed  upon  it 
to  slide  down  by  gravity.  liaise  the 
supporting  surface  till  the  style  on 
the  fork  just  touches  the  glass  plate 
as  it  slides  under  it.  Smoke  the 
upper  surface  of  the  sliding  glass,  set  the  fork  in  vibration  by 
a  blow  from  a  small  cork  mallet,  and  observe  the  tracing  pro- 
duced by  the  style  in  the  smoke  as  the  glass  glides  down  the 
plane.  Guides  made  of  glass  tubes  cemented  to  the  plane  will 
keep  the  moving  glass  from  turning  from  a  straight-line  course. 
Cement  a  coin  to  the  outer  end  of  the  fork,  and  note  the 
effect  on  the  pitch  as  shown  by  the  tracing  on  the  glass. 

Compare  the  tracings  given  by  two  forks  differing  an  octave 
in  pitch. 

In  Fig.  198  is  shown  another  device  for  studying  the  vibra- 
tions of  tuning-forks.     It  consists  of  a  wooden  cylinder,  A, 


FIG.  198. 


mounted  on  an  axis,  one  end  of  which,  B,  has  a  thread  upon 
it  working  under  the  small  wire  staple  which  keeps  it  in  place 


SOUND. 


275 


FIG.  199. 


on   the   standard.     The    fork   is    secured  by   its    stem   to   the 

block,   C,   clamped  to  the    base   by  a  screw,  D. 

By  this  means  the  fork  can  be  set  as  close  to  A 

as    may    be    desired.      The    cylinder   is 

smoothly  covered  with  smoked  paper,  on 

which  the  fork-style  traces  its 

record  as  the  cylinder  is  turned 

by  the  crank.     By  measuring 

the  rate  of  rotation  of 

A,  and   counting  the 

number  of  sinuosities 

made  by  the  fork,  the 

rate    of   the    fork    is 

easily  ascertained.  By 

using  a  second  block,  two  forks  may  be  compared. 

501.  Exercise.  —  To  study  sounds  produced  by  wind  in- 
struments, an  apparatus  constructed  as  follows  will  be  found 
quite  efficient :  Get  a  good  mechanic  to  turn  a  wooden  mouth- 
piece like  that  of  a  telephone,  but  somewhat  deeper  and  larger, 
shown  in  section  in  Fig.  200.  Glue  a  parchment-paper  dia- 
phragm, K,  across  it,  fastening  to  its  centre,  by  wax,  a  slender 
needle  with  its  point  curved  down.  Fasten  this  mouth-piece  to 
a  board,  B,  supported  in  an  inclined  position.  C  is  a  cross- 
piece  to  support  the  smoked  glass,  D.  M  is  a  guide  for  the 

glass.  C  is  given  such  an  in- 
clination that  the  glass  plate 
moves  along  by  gravity.  By 
changing  M,  the  part  of  the  plate 
under  the  marker  is  changed.  A 
stout  pin,  F,  keeps  the  needle 
from  being  dragged  out  of  posi- 
tion, and  jui  elastic,  H,  drawn  down  through  a  hole  in  B,  holds  the 


FIG.  200. 


276 


PRACTICAL   PHYSICS. 


needle  in  contact  with  the  glass  plate.  Any  sounds  produced 
in  front  of  and  close  to  A  will  move  the  needle  E,  and  cause 
a  characteristic  line  to  be  traced  on  D. 

502.     Exercise.  —  Cut  out   of   a  board  2.5  cm.    thick,  a 
strip  4  cm.  wide  and  25  cm.  long.     Near  one  end  bore  a  hole 


FIG.  201. 


2.5  cm.  in  diameter,  half-way  through  it.     Cut  a  second  piece 
of  the  same  width  and  5  cm.  long,  and  bore  into  it  a  similar 


SOUND. 


277 


hole.  Glue  these  two  pieces  together  so  that  the  two  holes 
face  each  other,  separating  them,  however,  by  a  membrane  of 
thin  rubber,  thus  forming  a  box  divided  into  two  parts  by 
this  membrane.  Nail  the  long  strip  to  a  piece  of  board  for  a 
support.  Bore  into  the  strip  A,  Fig.  201,  a  small  hole  leading 
into  the  box,  and  cement  into  it  a  short  glass  tube,  E.  In  B 
bore  two  such  holes,  and  cement  in  the  upper  one  a  jet- tube, 
and  in  the  lower  one  a  short,  straight  tube.  Connect  to  E  a 
piece  of  rubber  tubing,  with  a  funnel  for  a  mouth-piece. 
Connect  C  to  the  gas-supply.  On  turning  on  the  gas,  a  jet  can 
be  obtained  at  F.  Cut  a  cube  out  of  pine,  10  cm.  on  each  edge, 
as  M.  Insert  in  the  centres  of  two  opposite  faces  stout  wires, 
as  K  and  H.  Tie  on  the  lateral  faces  squares  of  looking- 
glass.  Rotate  this  apparatus  slowly  in  front  of  F,  and  observe 
the  image.  Compare  it  with  that  when  you  sing  in  the  funnel 
mouth-piece,  oo,  in  pool.  Ascertain  the  effect  of  changing  the 
pitch. 

Sing  the  vowel  o,  giving  it  the  pitch  of  the  note  B.  Sing  the 
vowel  a,  giving  it  the  pitch  of  F. 
Sing  the  vowel  a,  giving  it  the 
pitch  of  C.  Try  other  sounds. 
Draw  a  diagram  of  the  name- 
figure  in  each  case. 

503.  Exercise.  —  A  com- 
plete apparatus  for  the  optical 
exhibition  of  vibratory  motions 
is  shown  in  Fig.  202.  It  con- 
sists of  a  heavy  cubical  box  on 
two  adjacent  sides  of  which  are  secured,  by  means  of  bolts, 
the  blocks  A  and  F,  holding  the  tuning-forks  B  and  L. 
Slots  cut  in  the  frame  make  it  possible  to  give  the  forks  any 


FIG.  202. 


278  PBACTICAL    PHYSICS, 

desired  relative  position.  Small  pieces  of  mirror,  equal  in  size, 
are  cemented  to  the  lateral  faces  of  the  prongs  at  their  outei 
ends.  Flexible  steel  bars  might  be  used  in  place  of  forks, 
fastening  them  to  the  blocks  by  means  of  screws.  The  time 
of  vibration  of  the  forks  can  be  changed  by  fastening  small 
weights  to  the  prongs  with  wax. 

To  use  this  apparatus,  place,  a  few  metres  distant  from  the 
mirror  on  the  fork  at  E,  a  lamp  surrounded  by  a  dark  chimney, 
in  which  is  a  small  hole,  giving  a  small  line  of  light,  incident  on 
the  mirror.  Place  the  eye  so  as  to  see  the  image  in  this  mirror 
of  the  hole  in  the  chimney,  and  sot  the  fork  in  vibration.  The 


FIG.  203. 

image  becomes  an  elongated  line,  and  by  rotating  the  fork  a 
sinuous  line  is  produced,  varying  in  amplitude  as  that  of  the 
fork  changes.  By  receiving  the  reflected  ray  on  a  stationary 
mirror,  the  image  can  be  projected  on  a  screen,  the  distance  of 
the  screen  and  the  brightness  of  the  effects  being  governed  by 
the  intensity  of  the  light.  Clear  definition  can  be  secured  by  the 
aid  of  a  lens.  Fig.  203  exhibits  the  order  of  the  apparatus. 

Two  vibratory  motions  can  be  combined  by  placing  the  lamp 
so  that  the  beam  of  light  is  incident  on  the  mirror  on  the  fork  at 
D,  by  which  it  is  reflected  to  the  mirror  C,  on  a  second  fork, 
passing  thence  through  a  lens  to  the  screen.  By  moving  the 


SOUND, 


270 


block  A  to  the  position  M,  the  forks  can  be  made  to  vibrate  in 
the  same  plane  or  in  parallel  planes.  If  the  forks  are  in  unison 
the  luminous  line  on  the  screen  will  lengthen  and  shorten  at  regu- 
lar intervals,  but  if  they  vary  in  pitch  the  beats  resulting  from 
the  imperfect  harmony  will  be  heard,  and  at  the  same  time  a  curi- 
ous pulsating  character  will  distinguish  the  image.  Using  the 
forks  as  placed  in  the  figure,  the  combination  of  the  two  rectangu- 
lar vibratory  motions  is  effected,  the  image  obtained  depending 
on  the  interval  of  the  forks,  becoming  more  and  more  complex 
as  the  ratio  of  their  vibration-numbers  becomes  less  simple. 

In  Fig.  204  is  illustrated  a  cheap  substitute  for  the  foregoing 
apparatus,  the  forks  being  replaced  by  wooden  bars.  The  credit 
of  the  device  is  due  to  Mr.  George  M.  Hopkins. 

Select  a  box  about  60  cm.  square,  two  flat  springs  of  wood 
3  cm.  wide,  4  mm.  thick,  and  60  cm.  long,  or  metal  springs 
2.5  cm.  wide,  1.5  mm.  thick, 
and  of  the  same  lengtii  as  the 
wooden  ones.  Secure  these 
at  opposite  corners  by 
screws  to  blocks  2.5  cm. 
thick.  Cement  to  the  free 
ends  of  each,  and  in  the 
plane  of  vibration,  a  piece  of 
thin  cardboard,  having  a  slit 
2  mm.  wide,  parallel  with 
the  spring.  These  cards  are 
placed  as  near  each  other 
as  possible.  On  one  of  the 
springs  is  a  sliding-weight 
of  lead,  with  a  set-screw, 
so  that  the  time  of  vibration  can  be  changed  when  necessary. 
If  these  springs  are  now  set  in  vibration,  the  operator  on  look- 


FIG.  204. 


280 


PRACTICAL   PHYSICS. 


ing  at  the  lamp  through  the  two  slits  will  see  a  band  of 
light,  the  form  depending  on  the  relative  rates  of  the  two 
springs. 

By  placing  a  lamp  on  one  side  of  the  slotted  cards,  and  a 
lens  on  the  other,  an  image  can  be  projected  on  the  screen. 
The  figures  obtained  are  known  as  Lissajou's  curves.  In  the 
next  article  the  same  figures  are  produced  by  means  of  Black- 
burn's pendulum. 

504.     Exercise.  —  Construct  a  frame  like  the  one    shown 

in  Fig.  205.  The  height 
should  be  a  little  over 
1  m.  The  pendulum-bob 
is  supported  by  a  double 
cord  passing  through  the 
frame,  and  winding  round 
a  violin-key  inserted  in 
the  centre  of  the  cross- 
piece,  so  that,  by  turning 
the  key,  the  bob  can  be 
raised  or  lowered.  Slid- 
ing on  the  cord  is  a 
thick  leather  button,  r. 
The  bob  may  be  either 
a  small  glass  funnel, 
set  into  a  heavy  lead 
disk,  or,  what  is  better, 
a  lead  disk  having  a 
diameter  of  3  cm.  and  a 
depth  of  4  cm.,  the  inte- 
rior being  funnel-shaped,  with  a  circular  opening  in  the  bottom 
1  mm.  in  diameter.  Fine  sand  placed  in  the  bob  will  run  out 


FIG.  205. 


SOUND,  281 

as  the  bob  swings,  and  will  mark  out  on  a  board  placed  beneath 
it  the  path  described. 

Set  the  leather  slide  250  mm.  above  the  centre  of  gravity  of 
the  bob,  turn  the  violin-pin  till  the  whole  pendulum  is  1  m. 
long,  and  swings  about  5  mm.  above  the  paper  ;  fill  the  dish  with 
sand,  draw  it  to  one  side  over  a  line  making  an  angle  of  45°  at 
the  centre  with  that  joining  the  supports.  Try  in  succession  the 
following  positions  for  the  slide:  444.4  mm.,  562.5  mm.,  640 
mm.,  694.4  mm.,  734.6  mm.,  765.6  mm.,  790.1  mm.,  the  length 
of  the  pendulum,  as  a  whole,  being  kept  at  1  m.  If  the  above 
lengths  are  not  accurately  secured,  the  pendulum  will  fail  to 
retrace  the  first-formed  curve  as  it  continues  vibrating.  Draw 
diagrams  of  the  figures  obtained. 

An  examination  of  the  apparatus  will  reveal  the  fact  that  it 
consists  of  two  pendulums,  one  of  them  1  m.  long,  swinging  in 
a  plane  at  right  angles  to  the  supporting  bar,  the  other  a  shorter 
pendulum,  with  its  point  of  suspension  at  the  leather  slide, 
swinging  in  a  plane  forming  any  angle  at  pleasure  with  the 
plane  of  vibration  of  the  longer  pendulum.  It  will  also  be 
noticed  that  the  ratios  of  the  lengths  of  the  pendulums  in  the 

1       4       9      16    25     36     49     64 
different   cases   are  — ,  — ,  — ,  — ,  — ,  ^,  -^,  ^   respec- 

tively.  What  must  be  the  ratios  of  their  times  of  vibration? 
The  curve  obtained  in  each  case  is  from  the  composition 
of  two  simple  harmonic  motions.  The  pendulum  returns  to 
the  starting-point  after  a  definite  number  of  oscillations,  when 
the  periods  are  commensurable.  When  the  periods  are  incom- 
mensurable the  pendulum  never  returns  to  the  starting-point, 
and  consequently  the  curve  is  not  retraced. 


282  PRACTICAL    PHYSICS. 

XIX.      VOCAL    ORGANS. 

505.  Apparatus.  —  Glass  Tube,  Sheet  Rubber,  etc. 

506.  Exercise.  —  Roll  around  the  end  of  a  glass  tube  a 
strip  of  thin  india-rubber,  leaving  about  2  cm.  of  it  projecting 
beyond  the  tube.     Take  two  opposite  portions  of  the  projecting 
part  in  the  fingers,  and  stretch  it  so  that  a  slit  is  formed.     Now 
blow  through  the  tube,  and  a  sound  will  be  produced.     Ex- 
plain.     Ascertain  the  effect  of  varying  the  tension  of  the  rub- 
ber.    This   device    is  a  rough   representation   of   the   human 
larynx. 

507.  Exercise.  —  Sing  some  note  of  the  musical  scale,  and, 
without  changing  the  form  of  the  mouth-cavity,  hold  near  it,  in 
a  horizontal  position,  with  the  prongs  over  each  other,  the  free 
ends  of  a  vibrating  fork  of  the  same  pitch  as  the  note  sung. 
Alter  the  shape  of  the  mouth-cavity  and  repeat.     Inference. 


LIGHT, 


283 


CHAPTER   VII. 


LIGHT. 


I.     SOURCES    OF  LIGHT. 

508.  Apparatus.  —  Porte   Lumiere  Magic  Lantern,  etc. 

509.  Exercise.  —  As  parallel  rays  of  considerable  intensity 
are  required  for  many  of  the  experiments  with  light,  below  are 
described  several  ways  of  obtaining  such  a  light. 

First  Method.  —  Sunlight  is  brighter_than_any  artificial  light, 
and  a  horizontal  beam  can  be  re- 
flected into  the  work-room  through 
a  south  window  by  means  of  a 
Porte  Lumiere.  One  can  be  pur- 
chased of  dealers  in  physical  ap- 
paratus for  about  $5,  and  can  be 
constructed  at  even  a  less  outlay, 
as  follows :  — 

Procure  a  piece  of  pine  board 
as  long  as  the  width  of  the  win- 
dow, and  about  60  cm.  wide.  In 
it  cut  a  round  hole  12  cm.  in  diam- 
eter, the  centre  of  which  should  be 
the  centre  of  the  line  parallel  to  the 
edge  of  the  board,  and  20  cm.  from 
the  bottom.  On  one  face  of  the  board,  on  opposite  sides  of 


B 


Fie.  206. 


284 


PRACTICAL    PHYSICS. 


FIG.  207. 


the  centre  of  the  hole  T,  and  having  their  inner  faces  15 
cm.  apart,  fasten  two  wooden  arms,  DE,  32  cm.  long,  sup- 
ported by  iron  braces,  C.  Figs.  206,  207.  Pivot,  by  screws, 

between  their  outer  ends,  a 
rectangular  board,  FH,  2  cm. 
thick  and  15  cm.  square,  mak- 
ing the  distance,  DE,  31  cm. 
Cut  a  half-round  piece,  K, 
5  mm.  thick,  with  a  radius  of 
7  cm.,  and  fasten  it  by  slender 
screws  to  the  rectangular  piece, 
LM,  25  cm.  by  15  cm.  QN 
is  a  hard- wood  cylinder,  2.5 
cm.  in  diameter  ;  it  may  be  cut 
from  an  old  broom-handle. 
In  one  end,  as  shown  at  O, 
cut  a  slot  so  that  it  will  clasp 

the  piece  K,  to  which  it  is  to  be  secured  by  a  bolt,  around  which 
it  is  free  to  turn,  with  slight  friction.      S  is  a  triangular  block, 
the  shape  of  which  is  determined  by  the  method  illustrated  in 
Fig.   208.     On  a  large  sheet  of 
paper  lay  off  the  lines  DE  31  cm., 
and  DA  40  cm.,  forming  a  right 
angle  at  D,  a  point  corresponding 
to  the  centre  of  the  hole  T.     At 
E,   with   a  protractor,  make  the 
angle  DEQ  equal  to  the  latitude 
of  the  place.     Where    EQ   cuts 
DA  is  the  centre  of  the  hole  to 
be   bored   for   QN.      The  upper 
angle  of  the  piece  S  is  evidently 
equal  to  the  angle  DEQ.      Cut 


FIG.  208. 


LIGHT.  285 

this  piece  S  and  fasten  it  to  AD,  then  bore  the  hole  for  QN  per- 
pendicular to  the  upper  face  of  S.  P  is  a  wooden  washer,  pinned 
to  QN,  to  serve  as  a  shoulder,  and  is  so  placed  that  QN  extends 
through  the  board  far  enough  to  bring  the  lower  edge  of  LM  a 
few  centimetres  above  the  top  of  the  hole  T.  R  is  a  pin  at 
right  angles  to  QN,  for  convenience  in  turning  it.  On  the  front 
of  both  LM  and  FH  fasten  a  good,  plane  mirror,  completing 
the  apparatus. 

Place  this  porte  lumiere  in  a  south  window,  with  the  board 
in  a  vertical  position.  Determine  by  trial  the  inclination  of 
the  mirrors  so  that  sunlight  incident  on  LM  is  reflected  to 
FH,  and  from  it,  in  a  horizontal  line,  through  T.  Now,  by 
turning  QN  on  its  axis,  the  beam  of  light  can  be  kept  in  one 
place,  notwithstanding  the  changing  position  of  the  sun. 

QN  is  parallel  to  the  polar  axis  when  the  porte  lumiere  is  in 
position.  The  angle  between  LM  and  QM  changes  with  the 
sun's  angular  distance  from  the  equator,  called  its  declination. 
If  the  declination  is  represented  by  d,  then  the  angle  between 

ML  and  QN  equals — .       It  will  be  found   convenient  to 

graduate  the  piece  K  to  degrees  to  aid  in  setting  LM. 

Second  Method.  —  The  best  artificial  lights  are  the  electric 
of  the  arc  type  and  the  lime  light.  For  a  great  many  experi- 
ments, however,  a  powerful  kerosene-lamp  will  be  found  suf- 
ficient. With  either  of  these  lights,  means  will  have  to  be 
adopted  to  render  the  rays  parallel.  To  do  this,  proceed  as 
follows :  Place  the  light  in  a  large  wooden  box,  provided  witli 
holes  in  both  the  bottom  and  the  top  for  ventilation.  The 
depth  of  the  box  must  be  such  that  the  heat  from  the  lamp 
will  not  set  it  on  fire.  In  one  face  of  the  box,  exactly  opposite 
the  flame,  cut  a  circular  opening,  about  10  cm.  across,  depend- 
ing on  the  size  of  the  lens.  Tack  across  this,  on  the  inside t 


286 


PRACTICAL    PHYSICS. 


a  glass  plate  to  cut  off  the  heat  from  the  lens,  which,  mounted 
in  a  wooden  frame,  Fig.  209,  is  tacked  over 
the  opening  on  the  outside.  This  lens  had 
better  be  plano-convex,  and  have  a  focal  dis- 
tance of  15  cm.  The  light  must  be  situated 
at  its  focus,  and  be  incident  on  its  plane 
surface. 

Third  Method.  —  The  common  magic  lan- 
tern, by  removing  the  objective  and  adjusting 
the  condensers,  can  be  made  to  give  a  very 

satisfactory  beam.     This  instrument  has  been  so  improved  of 


FIG.  20.». 


FIG.  210, 


late  that  in  some  of  its  forms  it  is  now  capable  of  giving  a 
light  from  the  use  of  kerosene  varying  from  50  to  350  candle- 
power.  Fig.  210  shows  one  of  the  simplest  in  form  and  best 
in  construction. 


LIGHT. 


287 


FIG.  211. 


II.     RECTILINEAR    PROPAGATION    OF    LIGHT. 

510.  Apparatus.  —  Cardboard,  Tapers,  Candles,  etc. 

511.  Exercise.*  —  Support  with  retort  clamps  on  a  table 
two  small  sheets  of  cardboard  in  vertical  parallel  planes.     In 
the  centre  of  one  of  them 

cut  a  hole  2  mm.  in  diam- 
eter (Fig.  211),  and  place 
in  front  of  it,  at  a  distance 
of  a  few  centimetres,  a 
lighted  candle  or  lamp. 
Compare  the  images  of  the 
source  of  light  formed  on 
the  second  sheet  of  card- 
board as  you  vary  the  rela- 
tive distances  between  the 

three  objects.     Ascertain  the  effect  of  changing  the  shape  of 
the  aperture,  and  also  the  size  of  it. 

Surround  the  light  with  a  cylinder  of  cardboard  having  a 
small  hole  2  mm.  in  diameter  opposite  the  flame.  By  changing 
the  position  of  this  cylinder  light  may  be  taken  from  any  part 
of  the  flame.  Now  place  in  front  of  this  opening  a  sheet  of 
cardboard  with  an  aperture  5  mm.  square.  Behind  this,  and 
distant  from  it  a  few  centimetres,  set  the  second  sheet.  Observe 
the  image  formed  on  it  and  mark  its  position.  Move  the  cylin- 
der surrounding  the  light  so  as  to  take  light  from  a  different 
part  of  the  flame,  and  again  note  the  character  and  the  position 
of  the  image.  In  this  way  take  light  from  such  points  of 
the  flame  as  when  joined  will  give  an  outline  of  the  flame, 
being  careful  to  move  neither  the  cardboard  screens  nor  the 

*  All  those  experiments  which  require  a  dark  room  are  marked  with  an  asterisk. 


288 


PRACTICAL    PHYSICS. 


light.  Now  join  the  centres  of  the  images  and  compare  the 
figure  with  that  of  the  flame.  Remove  the  cylinder  and  note  the 
position  of  the  image.  Of  what  do  you  find  the  image  to  be  com- 
posed ?  In  what  way  does  the  size  and  shape  of  the  aperture  af- 
fect the  image  ?  Write  a  full  explanation  of  the  whole  subject. 

512.  Exercise.*  — Ascertain  why  an  image  of  every  object 
is  not  seen  imprinted  on  every  other  object  in  accordance  with 
the  principle  governing  the  formation  of  images  through  small 
apertures,  any   point   in   space  being   considered    as    such    an 
aperture. 

Set  up  an  apparatus  as  in  the  last  experiment.  Cut  a  large 
hole  in  the  cardboard  next  to  the  light  and  cover  it  with  tin 
foil.  Make  a  pin-hole  through  the  foil  and  observe  the  image 
of  the  flame  formed  on  the  screen.  Make  other  pin-holes  and 
observe  the  positions  of  the  images.  Keep  increasing  the  num- 
ber till  the  foil  is  full  of  holes  and  observe  the  effect.  Inference. 

513.  Exercise.*  —  Cut    out    of    cardboard    two   squares 

18  cm.  and  3  cm.  on  an  edge  respec- 
tively, and  mount  them  on  supports. 
A  simple  way  would  be  to  secure 
them  with  sealing-wax  to  a  heavy 
strip  of  cardboard  tacked  to  the  edge 
of  a  block  (Fig.  212).  Place  these 
squares  successively  between  a  large 
fan-shaped  flame  and  a  screen  made 
of  cardboard  supported  vertically  and 
parallel  to  the  square.  Compare  the 
shadows  cast  by  these  squares  on 
the  screen  when  the  flame  is  parallel 

to  them.     Determine  the  effect  of  placing  the  flame  edgewise  to 

the  square. 


LIGHT.  289 

Make  a  pin-hole  through  the  screen  in  the  darkest  part  of  the 
shadow  and  look  through  it  toward  the  flame.  Try  a  hole  in 
the  lighter  part  of  the  shadow.  Try  one  in  the  line  separating 
the  light  from  the  dark.  Try  one  wholly  without  the  shadow. 

Write  out  a  full  explanation  of  shadows  based  on  the  facts 
developed  by  these  experiments. 

III.    PHOTOMETRY. 

514.  Apparatus.  —  Cardboard,    Lamps,     "White    Screens, 
Candles,  etc. 

515.  Exercise.*  —  Cut  from   cardboard   three  squares,  4 
cm.,  8   cm.,  and  12  cm.,  respectively,  on  an  edge,  mounting 
them  as  directed  in  Art.  513,  making  the  length  of  support 
such  that  their  centres  are  each  at  the  same  distance  above  the 
table  as  the  light-emitting  point  to  be  used  in  the  experiment. 
Place  around  the  lamp  a  paper  cylinder,  and  in  it  cut  a  square 
hole  opposite  the  centre  of  the  flame,  but  smaller  than  its  least 
dimensions.     Now  set  the  largest  square  facing  the  aperture 
and  distant  from  it  about  a  metre.     Between  it  and  the  light 
stand  the  medium-sized  one,  finding  by  trial  the  place  where  it 
just  cuts  off  all  the  light  from  the  largest.     In  like  manner 
place   the   smallest  one   with   reference   to   the   intermediate. 
Measure  the  distance  of  each  screen  from   the   light.     Com- 
pare the  total  amount  of  light  incident  upon  the  smallest  screen 
with  that  incident  on  the  intermediate  when  the  first  is  removed, 
and  also  with  that  incident  on  the  largest  when  the  other  two 
are  removed.     Compare  the  amounts  on  equal  areas.     What 
effect  do  you  find  distance  to  have  on  intensity  of  light,  that 
is,  the  degree  of  illumination  of  equal  areas  ? 

516.  Exercise.*  —  Drop  a  little  hot  parafflne  or  beeswax 
on  a  sheet  of  unsized  white  paper,  and  warm  the  paper  till  the 


290 


PRACTICAL    PHYSICS. 


wax  has  thoroughly  soaked  into  it.  Give  the  spot  a  diameter 
of  about  3  cm.  Cut  from  this  paper  a  circular  piece  10  cm.  in 
diameter,  with  the  spot  in  the  middle,  and  cement  it  to  a  wire 
frame  provided  with  a  suitable  stem  for  supporting  it  in  a  ver- 
tical plane.  Lay  on  the  table  a  smooth  board  30  cm.  wide  and 
3.5  m.  long  ;  draw  lengthwise  of  it  a  straight  line,  and  graduate 
it  to  centimetres.  In  a  rectangular  block  bore  a  hole  large 
enough  to  admit  a  candle,  and  in  a  second  block  bore  four  such 
holes  in  line  and  1  cm.  apart.  Lengthwise  of  each  of  these 
blocks  draw  a  straight  line,  bisecting  the  holes,  to  be  used  in 
determining  the  position  of  the  candles  on  the  scale  on  the 
board.  Now  support  the  paper  disk  on  a  line  between  the  can- 
dles, finding  by  trial  a  position  for  it  where  the  wax  spot  is 
either  invisible  or  is  least  conspicuous  to  one  viewing  it  from 
a  position  in  line  with  the  board.  Read  off  on  the  scale  the 
distance  of  each  set  of  candles  from  the  disk.  Take  the  mean 
of  a  large  number  of  trials.  As  the  wax  spot  is  invisible 
when  the  two  surfaces  of  the  paper  disk  are  equally  illuminated, 
what  relation  do  you  find  existing  between  illuminating  power 
and  distance? 

517.     Exercise.*  —  Measure  the  candle-power  of  a  light. 
Support  a  white  paper  screen  in  a  vertical   plane.     About 


FIG.  213. 

10  cm.  in  front  of  it  fix  in  a  vertical  line  a  wooden  rod  1  cm. 
in  diameter,  by  the  aid  of  wax  (Fig.  213).     On  the  sanie  side, 


LIGHT.  291 

about  o()  cm.  from  the  screen,  place  a  lighted  sperm  candle  of 
the  size  known  as  "  sixes."  Now  place  the  light  to  be  meas- 
ured at  such  a  distance  that  the  two  shadows  of  the  rod  seen 
on  the  screen  are  of  equal  darkness.  Then  the  square  of  the 
ratio  of  the  distance  of  this  light  from  the  screen  to  that  of 
the  candle  is  the  candle-power  of  that  light.  Why  ?  Make 
several  determinations  of  the  candle-power  and  find  their  mean. 
Tabulate  the  results. 

518.  Exercise.*  —  Another  method  of  determining  the 
candle-power  of  a  light :  In  Art.  516  substitute  for  the  group 
of  four  candles  the  light  whose  candle-power  is  sought.  Now 
move  the  disk  till  the  waxed  spot  is  dimmest,  viewed  from 
either  side,  and  the  ratio  of  the  squares  of  the  distances  of  the 
lights  from  the  disk  will  be  the  candle-power. 


IV.    REFLECTION    OF    LIGHT. 

a.     Regular  Reflection. 

519.  Apparatus.  — Porte  Lumiere,  Cardboard,  Protractor, 
Glass    Mirror-Plate,    Prism,    Pane   of    Glass,    Glass  Jar,    Candle, 

etc. 

520.  Exercise.  —  Cut  six  blocks  of  wood,  each  4  by  6  by 
8  cm.,  and  two  pieces  of  board  8  by  4  by  .3  cm.     Tack  a  piece 
of  cardboard  of  the  size  of  a  postal  card  to  each  of  two  of  these 
blocks,  using   the    thin  wooden    strips    as    a    backing.     With 
a   large    darning-needle    make    a  hole    in    each  card    15   mm. 
from  the   end,  removing  with  a  sharp  knife  the   roughness  pro- 
duced.    Place  the  blocks  as  shown  in  Fig.  214.     On  the  centre 


292  PRACTICAL     PHYSICS. 

block  place  a  small  piece  of  mirror,  and  on  the  outside  block 
stand  a  lamp  or  candle  with  its  name  close  to  the  hole  in  the 
card.  With  one  eye  at  the  hole  in  the  other  card,  mark  with  a 

long  needle, 
fixing  it  iii 
place  with  soft 
wax,  where 
the  line  from 
the  image  of 
the  light 
pierces  the 
FIG'214-  mirror.  Now 

draw  on  a  sheet  of  paper  a  straight  line  whose  length  is  the 
distance  between  the  vertical  cards.  Erect  at  its  extremities 
perpendiculars  equal  to  the  height  of  the  holes  above  the  upper 
surface  of  the  blocks.  Lay  off  on  the  line  the  distance  of  the 
marked  point  on  the  mirror  from  one  of  the  cards,  and  join 
the  point  with  the  extremities  of  the  perpendiculars.  Erect  a 
perpendicular  at  this  point,  and  measure  with  a  protractor 
the  angles  between  it  and  the  oblique  lines.  Make  several 
trials  of  locating  the  point  on  the  mirror,  and  hence  get  several 
measurements  of  these  angles.  Inference. 

521.  Exercise.  —  Determine  the  law  for  the  reflection  of 
light. 

First  Method.  —  On  one  end  of  a  smooth  board,  32  cm.  wide 
by  60  cm.  long,  draw  a  circle  30  cm.  in  diameter,  and  divide  it 
into  degrees  by  means  of  a  protractor.  Pivot  at  the  centre  two 
wooden  arms  (Fig.  215).  Glue  to  the  top  one,  and  at  right 
angles  to  it,  a  strip  of  thin  board  2  cm.  by  3  cm.,  with  one  sur- 
face blackened  and  exactly  in'  line  with  the  axis  on  which  the 
arms  turn.  Cement  to  this  vertical  strip  a  piece  of  mirror  through 


LIGHT.  293 

the  amalgam  of  which  is  cut  a  narrow  line  ;  this  line  when  the 
mirror  is  in  place  must  be  exactly  in   the  axis.     To  the   outer 
end  of  the  under  arm, 
or    pointer,    fasten    a 
needle  in  a  normal  to 
the  plane  of  the  gradu- 
ated   circle.       To    the 
end  of  the  board  far- 

Fiu.  215. 

thest  from  the  gradu- 
ated circle  tack  a  rectangular  piece  of  cardboard,  through 
which,  at  a  point  about  1.5  cm.  above  the  board,  is  a  hole  1  mm. 
in  diameter.  The  free  ends  of  the  arms  should  be  bevelled, 
and  a  line  drawn  on  this  bevelled  portion,  which,  if  continued, 
would  pass  through  the  axis.  Now  place  the  hole  in  the  card- 
board, the  line  of  the  mirror,  and  the  mark  on  the  outer  end  of  the 
mirror-arm  in  such  a  position  that  the  line  on  the  mirror  bisects 
the  image  of  the  hole,  and  record  the  reading  of  the  mirror- 
arm.  Then  move  this  arm  a  few  degrees  and  bring  the  other 
arm  around  so  that  the  image  of  the  vertical  needle,  as  seen 
through  the  hole  in  the  cardboard,  coincides  with  the  line  on 
the  mirror.  Compare  the  angle  through  which  the  mirror- 
arm  was  moved,  with  that  between  the  needle-arm  and  the 

i 

second  position  of  the  mirror-arm,  as  shown  by  the  cir- 
cular scale.  Obtain  the  mean  of  a  number  of  trials  made 
at  different  parts  of  the  scale.  What  law  expresses  the 
results  ? 

Second  Method.  —  On  a  smooth  board  about  1  m.  by  30  cm. 
draw  a  straight  line  half-way  between  the  ends.  Set  a  rec- 
tangular strip  of  mirror  10  cm.  by  20  cm.  in  the  normal  plane 
through  this  line,  fixing  it  in  position  by  means  of  a  clamp  or  a 
little  wax.  Set  in  front  of  this  mirror,  and  distant  from  it 
as  well  as  from  each  other  a  few  centimetres,  two  darning- 


294 


PRACTICAL    PHYSICS. 


FIG.  216. 


needles  by  sticking  them  in  the  board  and  normal  to  it, 
as  A  and  B  (Fig.  216).  Now  set  C  in  line  with  A  and  the 

image  of  B,  and  D  in  line  with 
/•*  B  and  the  image  of  A.     Then 

remove   the  mirror  and   draw 
\ 

lines  through  A  and  C,  and  B 

and  D.,  Measure  with  a  pro- 
tractor the  angles  these  lines 
make  with  the  line  of  the  mir- 
ror. Vary  the  position  of  A 
and  B  and  obtain  the  mean  of 
several  values  for  these  angles. 
If  each  of  these  angles  is  sub- 
tracted from  90°  we  have  either 
the  angle  of  incidence  or  the 

angle  of  reflection  in  each  case,  as  it  will  be  observed  that  C  is  in 
line  with  A  and  the  images  of  both  B  and  D,  and  I)  is  in  line 
with  B  and  the  images  of  both  A  and  C.  What  relation  is  here 
established  between  these  angles? 

To  insure  greater  accuracy  the  needles  which  locate  lines 
should  not  be  placed  very  close  together. 

522.     Exercise.  —  Measure  the  angle  of  a  prism. 

First  Method.*  —  Cut  a  slit  1  mm.  wide  and  3  cm.  long  in  a 
square  of  cardboard,  and  fasten  it  across  the  opening  of  the 
lantern,  or  porte  lumiere,  so  that  a  vertical  ribbon  of  light  is 
obtained.  Place  the  prism  with  the  angle  to  be  measured 
towards  the  opening  in  the  cardboard,  and  approximately 
bisected  by  the  central  plane  of  the  ribbon  of  light  (Fig.  217). 
Part  of  the  ribbon  of  light  will  be  incident  on  one  face  of  the 
prism  and  be  reflected  from  it,  and  the  other  part  will  be 
similarly  disposed  of  by  the  other  face.  Now  stick  perpendic- 


LIGHT. 


295 


tilarly  in  the  board  supporting  the  prism  two  darning-needles, 
Nj  and  N2,  one  on  each  side  of  the  prism  and  in  the  reflected 
beam.    Then  set  N3  and 
N4,  two  other  darning- 
needles,  in  the   centres 
of  the  shadows  cast  by 
N!  and  N2,  respectively, 


and     distant 
centimetres. 


several 
Remove 


the    prism,   draw  lines 

through     the     points 

marked  by  the  needles,  FlG  217 

and   measure    with   the 

protractor  the  angle   they  form    at  D.     Half  of  this  angle  is 

the  angle  of  the  prism,  since  EDF  =  EAF  +  AED  +  AFD  = 

EAF  -f  AEH  -+-  AFK  =  2EAF. 


FIG.  218. 


Second  Method.  —  Place  the  prism  on  the  stand  of  the  Spec- 
trometer (Fig.  218),  with  the  angle  to  be  measured  turned 
toward  the  slit,  the  plane  of  light  approximately  bisecting  the 


296  PRACTICAL    PHYSICS. 

angle.  Now  move  the  telescope  till  the  intersection  of  the 
cross- wires  is  exactly  on  the  image  of  the  slit  reflected ;  first 
from  one  face,  and,  secondly,  from  the  other  face  of  the  prism. 
The  difference  between  the  readings  for  these  two  positions, 
given  by  the  vernier  attached  to  the  telescope-arm  on  the 
horizontal  scale  around  the  edge  of  the  table  of  the  instrument, 
will  be  double  the  angle  of  the  prism. 

It  will  be  readily  seen  that  this  method  differs  from  the  first 
one,  simply  in  the  use  of  a  telescope  and  verniered  scale  to 
secure  more  accurate  determinations  of  the  angles  involved. 

b.    Diffused  Reflection. 

523.  Exercise.* — Find  the  effect  of  an  irregular,  surf  ace 
on  light. 

Let  a  beam  of  light  be  incident  successively  on  a  good 
plane  mirror,  a  tarnished  surface,  a  pane  of  window-glass, 
a  pane  of  ground-glass,  and  a  sheet  of  white  writing-paper. 
Compare  the  brightness  of  the  spots  of  light  formed  on  the 
wall  by  reflection  from  these  surfaces.  Inference. 

524.  Exercise.* — Fill  a  large  glass  jar  with  smoke  by 
burning  touch-paper  within   it.     Cover  up  the  top  of  the  jar 
with  a  piece  of  cardboard,  through  which  is  a  hole  1  cm.  in 
diameter.     Set  a  plane  mirror  at  an  angle  so  that  it  will  reflect 
a  beam  of  light  into  the  jar  through  the  opening  in  the  cover. 
Compare  the  effect  with  that  when  an  empty  jar  is  used.     Ex- 
plain. 

c.    Amount   of  Light   Reflected. 

525.  Exercise.*  —  Ascertain   if  the   amount   of  light  re- 
flected from  a  surface  is  affected  by  the  size  of  the  incident 
angle. 


LIGHT.  297 

Support  a  small  plane  mirror  in  a  retort-holder,  giving  it 
such  an  inclination  that  a  strong  beam  of  light  incident  upon 
it  is  reflected  to  the  surface  of  a  shallow  basin  filled  with  water, 
striking  it  obliquely.  By  varying  the  distance  of  the  water 
from  the  mirror,  as  well  as  the  inclination  of  the  mirror,  any 
incident  angle  at  the  surface  of  the  water  may  be  obtained  at 
pleasure.  Compare  the  brightness  of  the  reflection  from  the 
water  on  the  wall  as  given  under  different  angles.  Inference. 

526.  Exercise.*  —  Place  a  sheet  of  writing-paper  on  a 
table,  and  near  it  a  lighted  candle.  Find  a  position  for  the  eye 
where  an  image  of  the  candle  can  be  seen  in  the  paper,  and 
observe  the  size  of  the  angles  of  incidence  and  of  reflection. 
Inference. 


V.     MIRRORS. 

527.  Apparatus.  —  Plane  Mirrors,  Darning-Needles,  Small 
Iron   Rings,  Pane  of  Glass,  Bottle,  Candles,  Cardboard,  Protrac- 
tor, Glass  Tube,  Concave  and    Convex  Mirrors,  Porte    Lumiere, 
Lenses,  Small  White  Screens,  Spherometer,  Scale,  etc. 

a.    Plane    Mirrors. 

528.  Exercise.  —  Find  where  the  image  of  an  object  in  a 
plane  mirror  is  situated. 

First  Method. — Select  a  smooth  board,  about  1  m.  long  and  30 
cm.  wide,  draw  a  line  across  the  middle  of  it  and  support  a  plane 
mirror  in  the  normal  plane  containing  this  line,  either  by  means 
of  a  clamp  or  sealing-wax.  Set  a  darning-needle  perpendicular 
to  the  board,  about  15  cm.  in  front  of  the  mirror,  and  also 
a  second  one  in  an  exact  line  with  the  first  one  and  its  image 


298  PRACTICAL    PHYSICS. 

in  the  mirror  (Fig.  219),  at,  say,  30  cm.  from  it.  As  far 
as  possible  to  one  side  of  these  set  two  more  needles,  so  that 
the  line  of  sight  through  them  passes  exactly  through  the 

image  of  the  first  needle 
set.  Now  remove  the  mir- 

M  ^^^          ror  and  draw  lines  through 

the  points  marked  by  the 
needles,  producing  them  till 
they  intersect.  Measure 
the  distance  of  this  inter- 
section from  the  reflecting 
surface  of  the  mirror,  that 
is,  from  the  line  drawn 
across  the  board,  and  also 

measure  the  distance  of  the  first  needle  set  from  the  same 
point.  Make  a  number  of  trials  and  obtain  the  mean.  In- 
ference. 

Second  Method.  —  Procure  at  a  hardware  store  two  iron 
rings,  about  3  cm.  across.  Cement  across  them  fine  wires, 
forming  diameters  at  right  angles.  Draw  across  the  middle  of  a 
smooth  board,  2  in.  long,  a  straight  line,  and  a  second  one  length- 
wise of  the  board,  and  perpendicular  to  the  first.  Graduate  this 
last  line  to  half -centimetres  each  way  from  the  intersection. 

Secure  with  seal- 
ing-wax in  a  verti- 
cal plane  and  on  the 
zero-line  a  piece 
of  mirror,  10  cm. 
square,  with  the 
FlG  220  amalgam  removed 

from      the     upper 
half  (Fig.  220) .     Cement  each  ring  to  the  end  of  a  wire,  fixed 


LIGHT.  299 

vertically  in  a  small  block  of  wood,  the  length  of  wire  to 
be  such  that  the  centre  of  each  ring  is  5  cm.  above  the  board 
supporting  the  mirror.  Draw  on  the  block  in  the  plane  of  the 
ring  a  line  to  aid  in  obtaining  the  position  of  the  ring  on  the 
linear  scale.  Set  one  of  the  rings  behind  the  mirror,  distant 
from  it  several  centimetres,  and  the  other  one  in  front.  Now, 
the  upper  half  of  the  first  ring  can  be  seen  through  the  un- 
silvered  part  of  the  mirror  when  the  eye  is  placed  level  with 
the  line  dividing  the  silvered  from  the  unsilvered  part,  and 
the  lower  half  of  the  other  one  will  give  an  image  behind  the 
mirror.  Carefully  adjust  the  position  of  the  ring  in  front  of 
the  mirror  till  the  image  of  its  lower  half  forms  an  exact  con- 
tinuation of  the  upper  half  of  the  one  back  of  the  mirror, 
making  the  ring  and  cross  seem  complete  on  moving  the  eye 
either  to  the  right  or  the  left.  This  position  is  easily  deter- 
mined by  observing  that  when  the  front  ring  is  too  near  the 
mirror,  on  moving  the  eye  to  the  right  the  image  and  object 
will  appear  to  separate,  the  image  going  to  the  left ;  and  if  too 
far  from  the  mirror,  the  reverse  is  the  case.  Now  read  off  on 
the  scale  the  distance  of  each  ring  from  the  mirror.  Repeat 
the  experiment  several  times,  and  obtain  the  mean  of  the 
measurements.  Inference. 

529.  Exercise.*  —  Procure  a  large  pane  of  window-glass, 
say,  1*2  by  20.  Support  it  in  a  vertical  plane  back  of  a  rectan- 
gular opening,  smaller  than  the  glass,  cut  in  a  large  sheet  of 
cardboard.  The  planes  of  the  cardboard  and  glass  make  a 
small  angle  with  each  other  (Fig.  221).  Place  a  lighted  candle, 
L,  between  the  screen  and  the  glass,  leaving  the  image  alone 
visible  through  the  opening.  Behind  the  glass  set  a  large  bottle 
of  water,  finding,  by  trial,  a  position  where  to  one  standing  in 
front  of  the  opening  in  the  cardboard  the  candle  appears  to  be 


300 


PRACTICAL    PHYSICS. 


burning  within  the  bottle.    Compare  the  distances  of  the  candle 
and  the  bottle  from  the  glass  plate.     Inference. 


o 


FIG.  2-21. 

The  above  experiment,  in  addition  to  locating  the  apparent 
position  of  the  image  of  an  object  in  a  plane  mirror,  also  illus- 
trates one  method  of  producing  spectral  phenomena  on  the  stage. 

530.  Exercise.  —  Determine  the  law  for  the  number  of 
images  in  cases  of  multiple  reflection. 

Cut  out  of  mirror-plate  two  pieces,  each  15  cm.  square. 
Hinge  them  together  at  one  edge  by  pasting  a  strip  of  cotton 
across  the  backs  of  both.  Stand  them  vertically  on  a  sheet  of 

paper  on  which  is  drawn  a  protractor 
scale,  placing  the  axis  of  the  mirrors 
in  line  with  the  centre  of  the  circle 
(Fig.  222) .  Now  stand  a  lighted  taper 
between  the  mirrors,  and  count  the 
number  of  images  for  any  specified  an- 
gle of  the  mirrors.  Try  90 °,  60  °,  45  °, 
and  40  °.  Note  the  relation  sustained 
by  the  angle  of  the  mirrors  to  the  en- 
tire circle,  and  compare  in  each  case 
with  the  number  of  images.  Account 
for  so  many  images  being  visible. 
Place  two  such  mirrors  parallel,  and  note  the  number  of 


\ 


FIG.    222. 


LIGHT.  301 

images.  Explain.  Show  that  the  result  agrees  with  the  law 
governing  the  number  of  images. 

Note  the  image  of  a  candle  in  a  very  thick  mirror.  Explain. 
Verify  your  explanation  by  blackening  one  surface  of  a  thick 
piece  of  glass,  with  the  amalgam  removed,  and  observing  the 
image  of  the  candle  in  it.  To  blacken  the  glass  hold  it  in  the 
smoke  emitted  by  burning  turpentine  or  camphor. 

531.  Exercise.  —  Coat  with  asphaltum  varnish  a  glass  tube 
30  cm.  long  and  2.5  cm.  in  diameter.  Make  a  pin-hole  in  a 
small  piece  of  cardboard  ;  hold  it  across  one  end  of  the  tube, 
with  the  pin-hole  in  the  axis  of  the  tube.  Now,  with  the  open 
end  to  the  eye,  look  at  the  bright  sky.  Describe  the  appear- 
ance, and  account  for  it. 

6.     Curved   Mirrors* 

.  532.  Exercise.*  —  Determine  how  a  concave  mirror  dis- 
poses of  incident  light. 

First.  —  Let  a  small  beam  of  light  be  incident,  perpendicu- 
larly on  the  mirror.  The  floating  dust  will  mark  out  the  path  of 
the  rays,  showing  that  the  rays  are  reflected  through  a  point 
called  the  principal  focus.  Measure  the  distance  from  this  point 
to  the  vertex  of  the  mirror.  Twice  this  distance  gives  the  radius 
of  curvature,  and  hence  enables  you  to  locate  the  centre.  Mark 
both  of  these  points  in  front  of  the  mirror  with  pointers  held 
by  clamps,  or  by  wires  set  in  large  corks  for  supports. 

Sunlight  can  be  used  for  finding  the  principal  focus,  by  as- 
certaining the  point  of  greatest  intensity  of  light  in  front  of  the 
mirror ;  that  is,  where  the  light,  reflected  on  a  piece  of  card- 
board, produces  the  smallest  bright  spot. 

Secondly.  —  Let  a  pencil  of  light  diverging  from  a  point 
beyond  the'  centre  of  curvature  be  incident  on  the  mirror,  and 


302  PRACTICAL    PHYSICS. 

find  where  it  focuses  with  reference  to  the  centre  and  the  prin- 
cipal focus,  as  shown  by  the  illuminated  dust-particles.  In  like 
manner  locate  in  succession  the  focus  for  a  pencil  of  light 
diverging  from  the  centre,  from  a  point  between  the  centre  and 
the  principal  focus,  from  the  principal  focus,  and  from  a  point 
between  the  principal  focus  and  the  mirror. 

Tliirdly.  —  Let  a  converging  pencil  be  incident  on  the  mirror, 
and  determine  its  course  after  reflection. 

A  simple  way  to  obtain  a  diverging  pencil  for  the  above  ex- 
periments is  to  let  a  beam  of  light  be  incident  on  a  lens  having 
a  focal  distance  of  about  50  cm.  The  lens  will  refract  the 
light  through  a  point,  producing  a  pencil  diverging  from  its 
focus.  For  a  converging  pencil,  the  part  between  the  lens  and 
the  focus  may  be  used. 

533.  Exercise.*  —  Ascertain   the   properties  of   a  convex 
spherical  mirror. 

Proceed  as  in  the  last  experiment,  making  such  modifications 
as  the  problem  demands. 

534.  Exercise.*  —  Determine  the  character  of  the  images 
of  an  object  given  by  spherical  mirrors 

Support  the  concave  mirror  in  a  vertical  position  on  a  long 
table,  and  place  in  front  of  it  a  lighted  candle  at  a  distance 
greater  than  the  radius  of  curvature  of  the  mirror.  On  the 
same  side  of  the  mirror  support  a  small  paper  screen,  finding 
by  trial  a  position  for  it  where  a  sharply  defined  image  of  the 
candle  is  formed  on  it.  Compare  the  distances  of  the  object 
and  image  respectively  from  the  mirror;  also,  size,  position, 
etc.  Now  gradually  move  the  candle  nearer  to  the  mirror  and 
determine  the  character  of  the  image  for  each  new  position, 
particularly  when  the  light  is  at  the  centre  of  curvature,  between 
the  centre  and  the  principal  focus,  at  the  principal  focus,  and 
between  the  focus  and  the  mirror. 


LIGHT.  303 

In  the  case  of  the  convex  mirror,  what  is  the  character  of  the 
image?  Ascertain  the  effect  that  the  position  of  the  object  has 
upon  the  character  of  the  image. 

535.  Exercise.  —  Measure  the  radius  of  curvature,  and 
hence  the  focal  distance  of  a  concave  spherical  mirror. 

First  Method.*  —  Support  the  mirror  vertically  on  a  long 
table  ;  place  in  front  of  it  a  sheet  of  cardboard  in  which  is  cut 
a  hole  1  cm.  square.  Illuminate  the  opening  by  placing  a  lamp 
back  of  it,  and  place  a  screen  to  receive  the  image  of  it  formed 
by  the  mirror.  Move  the  screen  till  the  outline  of  the  image  is 
brightest  and  has  the  sharpest  outline.  Measure  the  distance 
of  the  object  from  the  mirror,  and  also  that  of  the  image.  If 
these  are  represented  by  a  and  b  respectively,  and  the  radius  by 
R,  then 


I  -    *    =   1  =  I  whence  R  =     2a^    and  f  = 

nth  TJ  ^  .17,  •' 


ab 


b    "   R~  f  a  +  b  '    a-\-b 

Second  Method.  —  Insert  a  small  piece  of  stiff  white  paper  in 
the  eye  of  a  darning-needle  to  serve  as  an  index,  and  at  the 
same  time  to  make  it  more  conspicuous.  Set  it  vertically  in 
front  of  the  mirror,  finding  by  trial  a  place  where  the  point  of  the 
paper  coincides  with  the  image  of  it  seen  in  mid-air.  Measure  the 
distance  from  the  pointer  to  the  vertex  of  the  mirror.  Obtain 
tii,'  average  of  several  trials  ;  the  result  will  be  the  radius  of 
curvature.  Why?  How  would  you  get  the  focal  distance? 

Third  Method.  — Place  the  spherometer  on  the  curved  sur- 
face, and,  proceeding  as  in  Art.  11,  obtain  the  altitude  of  the 
segment  that  would  be  cut  off  by  the  plane  of  the  three  legs  of 
the  instrument.  Let  h  =  this  altitude,  and  s  =  the  side  of  the 

equilateral  triangle  formed  by  the  feet.     Then  R  =  -—-  -I , 

6h         2 

a  relation  deduced  geometrically  from  the  properties  of  a  sphere. 


304 


PRACTICAL    PHYSICS. 


This  method  cannot  be  applied  to  the  ordinary  glass  mirrors, 
as  they  are  usually  plano-convex  lenses  silvered  on  the  convex 
surface. 

536.  Exercise.  —  Measure  the  radius  of  curvature  of  a  con- 
vex spherical  mirror. 

First  Method.  —  Locate  the  position  of  the  image  as  directed 
in  Art.  528.  Measure  the  distance  of  the  object,  and  also  the 
image,  from  the  vertex  of  the  mirror.  Then 

112  n         2ab 

— — -  =  — . ,  whence   H  =  — —  . 

b        a        R  a  —  b 

Second  Method.*  —  Cut  a  round  hole  5  cm.  in  diameter  in  a 
sheet  of  cardboard,  and  support  it  several  centimetres  in  front 

of  the  mirror  and  per- 
pendicular to  its  axis 
(Fig.  223).  Let  a  strong 
beam  of  light  be  inci- 
dent on  the  cardboard, 
part  passing  through  the 
opening,  making  a  round 
image  on  the  mirror,  and 

li  a    second    one    on    the 

PIG.  223.  ,     , 

cardboard,  by  reflection. 

Measure  the  diameter,  DE,  of  the  spot  on  the  screen ;  FH,  or 
AB  of  the  opening  or  spot  on  the  mirror ;  and  LK,  the  distance 
from  the  screen  to  the  mirror.  Then  if  AB  =  a,  DE  =  6,  LK 
=  c,  and  KC  =/=  JR,  we  have,  by  geometry, 


M 


B 


,  R_ 

"  ~ 


2ac 


Third  Method.  —  Employ  the  spherometer  as  in  Art.  535. 

537.   Exercise.*  —  Compare  as  to  brightness  and  sharpness 
of  outline  the  image  given  by  a  concave  mirror  when  the  light  is 


LIGHT, 


305 


cut  off  from  all  but  the  central  portion,  with  that  when  the 
whole  surface  of  the  mirror  is  used.  Bend  a  piece  of  bright 
tin  into  a  semicircular  form,  place  it  on  a  sheet  of  white  paper 
with  its  concave  surface  toward  the  light,  and.  notice  how  it 
reflects  the  rays.  Explain. 


VI.     SINGLE    REFRACTION    OF    LIGHT. 

538.  Apparatus.  —  Porte  Lumiere,  Rectangular  Battery-Jar, 
Protractor,   Cardboard,    Prisms,  Darning-Needles,  Spectrometer, 
Plane  Mirrors,   Globular  Receiver,   etc. 

539.  Exercise.* — Measure  the  index  of  refraction  of  a  liquid. 
Cover  one  face  of  a  large  glass  rectangular  battery-jar  with 

paper,  out  of  the  centre  of  the  covering  having  cut  as  large  a  cir- 
cle as  possible.  Across  this  circular  opening  draw  a  horizontal 
and  a  vertical  diameter  (Fig.  224) .  Graduate  the  margin  of  the 
circle  to  degrees,  the  ex- 
tremities of  the  vertical 
diameter  to  be  marked 
zero,  and  those  of  the 
horizontal  one  90° .  Pro- 
vide a  strip  of  card- 
board considerably  wid- 
er and  longer  than  the 
top  of  the  jar,  and  cut 
in  it,  cross-wise,  a  slit 

FIG.  224. 

2  mm.  wide  and  5  cm. 

long.  Fill  the  jar  with  water  exactly  to  the  horizontal  diame- 
ter of  the  circle.  Place  the  cardboard  containing  the  slit  on 
top  of  the  jar.  With  a  plane  mirror  supported  in  a  retort- 
holder  reflect  a  strong  beam  of  light  through  the  slit  at  such 


\\ 


306 


PRACTICAL    PHYSICS. 


an  angle  as  to  be  incident  on  the  liquid  exactly  back  of  the 
centre  of  the  circle.  Read  off  on  the  scale  the  angle  that  the 
incident  ray  makes  with  the  vertical,  and  also  that  made  by 
the  refracted  ray  seen  in  the  liquid.  Change  the  position  of  the 
slit  and  the  mirror  so  as  to  get  a  number  of  these  angular 
measurements  for  different  beams.  Divide  the  sine  of  each 
angle  of  incidence  (see  Table  XX.)  by  the  sine  of  the  corre- 
sponding angle  of  refraction,  and  the  average  of  these  quo- 
tients will  be  the  index  of  refraction. 

A  large  square  bottle,  or  a  tin  tank  with  one  glass  face,  may 
be  substituted  for  the  battery- jar.  In  using  the  battery- jar  it 
will  render  the  rays  more  distinct  to  cement  black  paper  on  the 
faces. 

Any  of  the  following  liquids  may  be  used  for  this  experi- 
ment: Water,  alcohol,  naphtha,  turpentine,  kerosene,  etc. 

540.     Exercise.  —  Determine  the   index   of    refraction   of 

glass. 

First   Method.*  —  Tack   across   the   opening   of    the    porte 

lumiere,  or  lantern,  a  piece  of   cardboard  in  which  is  cut  a 

vertical  slit  1  mm. 
wide  and  3  cm.  long. 
In  the  path  of  the 
ribbon  of  light  which 
passes  through  the  slit 
place  a  glass  prism 
of  known  angle  (see 
Art.  522),  supported 
Flo  225  on  a  smooth ,  hori- 

zontal    board,     with 

its  edges  parallel  to  the  plane   of  the   ribbon   of   light,    and 

intercepting  it  at  such  an  angle  that  it  suffers  the  least  deviu- 


LIGHT.  307 

tion  from  its  course  ;  a  result  recognized  by  slowly  turning  the 
prism  about  its  axis  till  the  bright-colored  image  on  the  wall 
departs  least  trom  the  line  of  light  before  it  suffers  refrac- 
tion. Now  set  perpendicularly  in  the  board  a  darning-needle,  N1? 
to  mark  the  place  where  the  light  is  incident  on  the  prism  (Fig. 
225).  Set  a  second  one,  N2,  in  the  shadow  cast  by  Nx.  Remove 
the  prism  and  set  a  third  one,  N3,  in  the  shadow  now  cast  by 
N\.  Draw  lines  through  the  points  marked  by  the  needles,  and 
measure  with  a  protractor  the  angles  between  them.  Make 
a  number  of  trials,  and  determine  their  average.  This  will 
be  the  angle  of  deviation  for  the  prism.  If  a  =  the  angle  of 
the  prism  and  d  —  the  deviation,  then  the  index  of  refraction, 

sin  A  (a-f-  d) 
of  i  =      — ^rr—t -. 

Kin  £a 

Second  Method.  —  Place  the  prism  on  the  stand  of  the  spec- 
trometer of  Art.  522,  a  form  in  which  the  telescope  is  attached 
to  a  movable  arm  carrying  an  index  moving  over  a  graduated 
circle.  Place  the  prism  in  the  position  of  least  deviation. 
This  is  found  by  observing  the  slit  through  the  telescope,  at  the 
same  time  slowly  turning  the  prism  till  the  dark  vertical  line 
seen  in  the  green  part  of  the  image  moves  out  of  the  field 
in  the  same  direction  on  turning  the  prism  either  way.  Now 
read  the  index  of  the  telescope-arm  when  the  cross-hairs  are 
exactly  on  the  dark  line  in  the  green.  If  not  visible,  use  the 
dark  line  in  the  yellow.  Then  remove  the  prism,  and  obtain 
the  reading  when  the  slit  is  in  the  field  of  the  telescope.  Ob- 
tain the  average  of  several  determinations  of  these  readings, 
and  their  difference  will  be  the  angle  of  deviation  for  the  prism. 
To  obtain  the  index  of  refraction,  apply  the  formula  of  the  first 
method. 

Obtain  the  index,  using  dark  lines  seen  in  other  colors  of  the 
spectrum. 


308 


PRACTICAL   PHYSICS, 


541.  Exercise.*  —  Using  the  apparatus  of  Art.  539,  place 
the    cardboard    against   the   end,  so  that  the  slit  is   near   the 
bottom  of  the  jar.     Now  place  a  plane  mirror,  so  as  to  throw 
a  beam  of  light  on  to  a  second  mirror  lying  on  the  table  close 
to  the  slit,  and  incident  at  such  an  angle  that  it  passes  through 
the  slit  into  the  liquid,  reaching  the  surface  opposite  the  centre 
of  the  circle.     Observe  the  course  of  the  light  after  incidence, 
taking  the  readings  on  the  graduated  scale.     Explain. 

Raise  the  slit,  changing,  accordingly,  the  position  of  the 
mirror  till  the  ray,  after  incidence,  passes  out  along  the  surface. 
Measure  the  angle  of  incidence,  thus  obtaining  the  critical  angle 
for  the  liquid.  Try  different  liquids. 

542.  Exercise.*  —  Procure  a  globular  receiver,  about  10 
cm.    in  diameter,  with  two  tubulures  (Fig.  226).     Close  each 
neck  with  good  corks,  through  which  pass  as  large  glass  tubes 

as  possible.  Coat  the  outside  of  the 
globe  with  black  varnish,  except  the 
area  included  within  the  small  circle, 
indicated  by  the  dotted  line,  op- 
posite the  neck  to  be  used  as  the 
horizontal  one.  Fill  the  globe  with 
water,  having  first  closed  the  horizon- 
tal tube  with  a  cork ;  connect  the 
upper  one  with  a  rubber  tube  to  a 
tank  supplying  water,  and  adjust  the 
apparatus  in  the  opening  of  the  porte 

lumiere  so  that  the  light  is  incident  on  the  unvarnished  part, 
and  all  light  is  cut  off  from  entering  the  room.  Now  remove  the 
stopper  from  the*  exit- tube,  and  notice  how  the  light  follows  the 
stream  of  water.  Explain.  A  strip  of  red  glass  placed  between 
the  globe  and  the  source  of  light  produces  a  very  striking  effect. 


FIG.  226. 


LIGHT. 


309 


543.  Exercise.*  —  Let  a  small  beam  of  light  be  incident 
perpendicularly  on  one  of  the  faces  about  the  right  angle  of 
what  is  known  as  the  right-angled  prism.     Observe  the  course 
of  the  light.     Explain. 

VII.    LENSES. 

544.  Apparatus.  —  Porte  Lumiere,  Convex   and   Concave 
Lenses,    Cardboard,    Scales,    Telescope,    Spherometer,     Candles, 

etc. 

545.  Exercise.  —  Measure  the  principal  focal  distance  of 
a  convex  lens. 

First   Method.  —  Tack  a  piece  of  cardboard,  about  15  cm. 
square,    across   one    end  of  a  common  lath  (Fig.  227).     Be- 
ginning at  the  cardboard,    lay  off  a  half -centimetre  scale  on 
the  wooden  strip.     Now 
hold    the  lens    on    the 
strip     parallel    to     the 
screen,   direct    the   ap- 
paratus toward  the  sun , 
and  slide  the  lens  along 
till  a  position  is  found 
where   the   light  forms 
the  smallest  and  bright- 
est image  of  the  sun  on  the  screen.     Read  off  on  the  scale  the 
distance   of  the   lens   from   the  screen  for  the   focal  distance 
required.      Obtain  the  mean   of  several  independent  determi- 
nations. 

Second  Method.*  —  Support  the  lens  in  a  vertical  plane,  plac- 
ing on  one  side  of  it  a  cardboard  screen,  and  on  the  other  a 
sheet  of  cardboard  with  a  circular  aperture,  1  cm.  in  diameter, 
having  two  threads,  mutually  perpendicular,  stretched  across 


FIG.  227. 


310  PRACTICAL    PHYSICS. 

its  centre,  and  illuminated  on  the  opposite  side  from  the 
lens  by  a  lamp  or  candle  placed  near  the  opening.  Adjust 
the  apparatus  so  that  the  centre  of  the  opening  lies  in  the 
principal  axis  of  the  lens.  Now  find  by  trial  a  position  for 
the  lens  between  these  sheets  of  cardboard  where  a  sharply 
defined  image  of  the  threads  is  formed  on  the  other  screen. 
Measure  the  distances  between  the  lens  and  the  image  and  ob- 
ject respectively,  representing  them  by  a  and  &,  then  the  focal 

distance  =  —   '—=-•     Obtain  the  mean  of  several  determinations. 
a-r-6 

This  method  neglects  the  thickness  of  the  lens.  As  this  is 
usually  small,  the  value  of  /  would  not  be  materially  altered. 

Third  Method.*  —  Using  the  apparatus  of  the  last  method, 
adjust  the  distances  so  that  the  image  and  object  are  equal  in 
size.  Then  one-fourth  of  the  distance  between  them  is  the 
focal  distance  of  the  lens.  Obtain  the  mean  of  several  deter- 
minations. 

Fourth  Method.  —  Focus  a  small  telescope,  as  a  common  spy- 
glass, on  some  object  so  far  distant  that  the  rays  from  it  may 
be  considered  as  parallel  without  sensible  error.  Now  place  the 
lens,  whose  focal  distance  is  to  be  measured,  in  front  of  the 
telescope,  and  look  through  the  two  at  some  figure  on  a  piece 
of  cardboard  held  in  a  clamp.  Move  the  cardboard  to  such  a 
distance  from  the  lens  as  to  be  clearly  visible.  The  distance  of 
the  cardboard  from  the  lens  is  the  focal  distance  sought.  Ob- 
tain the  mean  of  several  trials. 

Fifth  Method.  —  If  the  lens  has  sufficient  surface,  the  radius 
of  curvature  of  each  surface  can  be  determined  by  the  sphero- 
meter,  as  in  the  case  of  mirrors  (Art.  535).  Representing  by 
r  and  r'  the  radii  of  curvature  of  the  two  faces,  and  by  i,  the 

index  of  refraction,  then  f=— — T~/     , — ;V     The  average  in- 

L  —  1   \r  -f-  r  ) 


LIGHT. 


311 


dex  of  crown  glass  may  be  taken  as  1.5  without  sensible  error. 

2  rr* 
Hence, /=— q; — r     ^  koth  surfaces  have  the  same  curvature, 

then  r  =  r'  and/=r,  that  is,  the  focal  distance  equals  the  ra- 
dius of  curvature.  If  the  lens  is  plano-convex,  then  r'  =  oo 
and/=2?\  For  the  meniscus  lens  the  radius  of  curvature  for 
the  concave  surface  must  be  taken  as  negative. 


546.     Exercise.  —  Measure  the  principal  focal  distance  of  a 
concave  lens. 

First  Method.*  —  Cover  the  face  of  the  lens,  that  is  turned 
away  from  the  light,  with  paper,  in  which  is  cut  a  smooth,  round 
hole  2  cm.  in  diameter,  exactly  over  the  optical  centre.  Sup- 
port the  lens  so  that  a  beam  of  light  parallel  to  the  principal 
axis  is  incident  upon  it.  Hack  of  the  lens,  and  parallel  to  it, 
place  a  card- 
board screen. 
The  light,  after 
passing  through 
the  lens,  will 
diverge  as  if  it 
came  from  the 
principal  focus, 
and  will  form 
a  round  image 
on  the  screen. 

Hence,  if  we  measure  the  distance  AB  (Fig.  228),  the  diameter 
of  the  image ;  the  distance  CD,  the  diameter  of  the  aperture  ; 
and  the  distance  EH  from  the  lens  to  the  screen ;  we  can  com- 
pute the  focal  distance  EF,  neglecting  the  thickness  of  the  lens, 
as  it  is  usually  small.  Representing  these  distances  by  a,  6, 


Flo.  228. 


312  PRACTICAL    PHYSICS. 

and  c,  respectively,  we  derive  from  the  triangles  in  the  figure 
,       be 
/==^6- 

By  moving  the  screen  till  AB  =  2CD,  the  distance  of  the 
screen  from  the  lens  is  the  focal  distance. 

Try  both  ways,  obtaining  the  mean  of  several  determinations. 

Second  Method.  —  Place  in  contact  with  the  concave  lens  a 
convex  one,  making  the  combination  equivalent  to  a  convex 
lens.  Measure  the  focal  distance  of  the  combination,  as  in 

Ff' 

Art.  545,  and  also  of  the  convex  lens  alone.     Then  f=  •= — -,• 

f  — ./ 

in  which  F  is  the  focal  distance  of  the  combination,  and  /'  of 
the  convex  lens. 

Third  Method. — Employ  the  spherometer  as  in  Art.  545, 
making  the  r's  in  the  formula  negative  when  the  surface  is  con- 
cave. 

547.  Exercise.*  —  Ascertain   how  a   lens   disposes   of    a 
pencil  of  light. 

First.  —  After  determining  the  focal  distance,  support  the 
lens  in  a  clamp,  and  let  a  diverging  pencil  of  light  be  incident 
upon  it,  as  in  Art.  532.  Ascertain  where  the  rays  focus  when 
the  light  diverges  from  a  point  beyond  twice  the  focal  distance, 
at  twice  the  focal  distance,  at  less  than  twice  but  beyond  the 
focus,  at  the  focus,  and,  finally,  between  the  focus  and  the  lens. 
Test  both  convex  and  concave  lenses. 

Secondly.  — Try  a  converging  pencil.  In  the  case  of  a  con- 
cave lens  vary  the  degree  of  convergence  by  using  lenses  of 
different  focal  distances  to  produce  the  pencil  of  light. 

548.  Exercise.*  —  Determine  the  character  of  the  images 
formed  by  lenses. 


LIGHT.  313 

First.  —  Place  on  a  long  table  a  cardboard  screen,  a  mounted 
convex  lens  of  known  focal  distance,  and  a  lighted  lamp  or 
candle,  arranging  them  in  the  order  named,  and  with  their 
centres  in  the  same  horizontal  line.  Place  the  light  succes- 
sively at  more  than  twice  the  focal  distance,  at  twice  the  focal 
distance,  at  less  than  twice  but  beyond  the  focus,  and,  finally, 
between  the  focus  and  the  lens,  determining  in  each  case,  if 
possible,  the  position  of  the  screen  where  the  well-defined  image 
of  the  flame  is  formed  upon  it.  Compare  the  image  in  each 
case  with  the  object  as  regards  size  and  position. 

Secondly.  —  Compare  the  image  formed  when  a  lens  of 
small  diameter  is  used  with  that  when  one  considerably 
larger  is  employed  and  adjusted  to  give  an  image  of  the 
same  size. 

Thirdly.  —  Cover  a  lens  with  a  paper  disk  in  which  is  cut 
a  ring  of  holes  near  the  circumference,  and  also  a  ring  near 
the  centre.  Mount  the  lens  so  that  a  beam  of  light  is  inci- 
dent upon  it  and  focuses  on  a  screen.  Ascertain  if  the  outer 
ring  of  holes  focuses  at  the  same  distance  from  the  lens  as 
the  inner  row. 

Fourthly.  —  Compare  the  definition  of  the  image  formed 
when  light  is  admitted  through  the  whole  lens  with  that  given 
when  the  light  incident  on  the  outer  edge  of  the  lens  is  cut 
off  by  a  paper  ring  placed  over  it. 

Fifthly.  —  Study  the  images  given  by  a  concave  lens. 

549.  Exercise.  —  Measure  the  magnifying  power  of  a 
lens. 

First  Method.  —  Measure  the  focal  distance  of  the  lens,  then 

25cm. 
the  magnifying  power  =    — j h  1,  in  which  25  cm.  is  taken 

as  the   distance  of  distinct  vision. 


314 


PRACTICAL    PHYSICS. 


Second  Method.  —  Focus  the  lens  on  a  finely  divided  scale 
securing  clear  definition.  Place  a  second  scale  at  the  dis- 
tance of  distinct  vision,  25  cm.  Now  look  with  one  eye 
through  the  lens  at  the  one  scale,  and  with  the  other  eye  at 
the  second  one.  On  the  eye's  becoming  accustomed  to  the 
conditions  of  the  experiment,  the  magnified  image  of  one 
scale  will  be  seen  superposed  on  the  other.  Count  how  many 
divisions  of  the  magnified  scale  exactly  cover  a  certain  num- 
ber on  the  other.  Divide  the  latter  by  the  former,  the 
quotient  will  be  the  magnifying  power. 

VIII.      DISPERSION. 

550.  Apparatus.  —  Porte  Lumiere,  Cardboard,  Lenses, 
Prisms,  Glass  Bulb,  etc. 

551.    Exer- 
cise.* —  Tack 

across  the  open- 
ing of  the  porte 
lumiere,  or  lan- 
tern, a  piece 
of  cardboard  in 
which  is  cut  a 
very  narrow  slit 
with  straight 
smooth  edges. 
Project  with  a 
convex  lens  of 
about  30  cm. 
focus  an  image 
of  this  slit  on 
a  distant  white 
screen.  Close  to  the  lens,  between  it  and  the  screen,  place 


FIG.  229. 


LIGHT.  315 

a  prism  of  crown  glass  (Fig.  229),  of  60°  angle,  and  change 
the  position  of  the  screen,  keeping  it  at  the  same  distance 
from  the  lens,  to  a  position  where  the  light  falls  perpendicularly 
upon  it.  Turn  the  prism  around  till  the  least  deviation  is 
secured.  Describe  the  image. 

Compare  the  spectrum  given  by  a  prism  of  crown  glass  with 
that  given  by  one  of  flint  glass,  or  one  of  carbon  disulphide 

Try  two  prisms,  setting  the  second  one  behind  the  first, 
with  its  base  turned  in  the  same  direction. 

To  make  a  carbon  disulphide  prism  proceed  as  follows  :  — 

Cut  off  the  ends  of  a  stout  glass  tube,  4  cm.  in  diameter, 
by  planes  inclined  to  each  other  at  an  angle  of  60°,  and 
their  line  of  intersection  perpendicular  to  the  axis  of  the  tube 
(see  page  354).  Grind  the  ends  smooth  on  a  flat  sand- 
stone. Drill  a  hole  through  the  side  of  the  tube.  This 
hole  had  better  be  made  before  cutting  off  the  ends,  to 
avoid  lost  labor  from  a  possible  breaking  of  the  tube  in 
drilling  it.  Cement  with  good  glue  two  pieces  of  the  best  of 
thin  plate-glass  on  these  faces  ;  mirror-plate  with  the  amal- 
gam scratched  off  is  the  best,  as  it  is  more  likely  to  be  true. 
When  dry,  fill  the  angles  on  the  outside  between  the  glass 
plate  and  the  tube  with  a  cement  made  of  glue  dissolved  in 
common  molasses  by  the  aid  of  heat.  Now  fill  the  cell  through 
the  hole  In  the  side,  cork,  and  cover  the  cork  with  cement. 

The  cell  must  not  be  filled  in  the  vicinity  of  a  flame,  as 
carbon  disulphide  is  very  inflammable. 

552.  Exercise.*  —  Project,  as  in  the  last  experiment,  a 
spectrum  of  some  strong  light  on  a  screen.  Cut  a  hole 
through  this  screen  so  that  one  color  passes  through  and  is 
incident  on  a  second  prism.  Ascertain  if  any  new  colors  are 
obtained  by  the  second  dispersion.  Inference. 


\V\ 

ith    ^SJy\ 

ide. 


316  PEACTICAL    PHYSICS. 

White  printing-paper  or  cotton  cloth,  pasted  over  a  light 
wooden  frame,  will  make  a  suitable  screen. 

553.  Exercise.*  —  Project,    as    directed    in    Art.    551,  a 
spectrum   on  a  screen,   using  a  short  slit.     Behind  the  prism 
place    a    second    prism  with   its    edges    perpendicular  to   the 
edges   of  the  first,    and  in  a  position  to  receive1  the  light  on 
issuing  from  the  first.     By  this  arrangement  there  will  be  in- 
cident on  the  second  prism   rays   of   each  color,  each  one  by 
itself,    making   it   possible   to  determine  whether  a  prism   re- 
fracts each  color  alike  or   not ;    for  if  it  does,  the  new  spec- 
trum will  occupy  a  position  parallel  to  the  old  one.     Inference. 

554.  Exercise.*  —  Project  a  spectrum  on  a  screen  as  di- 
rected in  Art.  551.      Now  place  a  second  prism  like  the  first 
behind  the  first,  but  reversed  in  position.     Observe  the  char- 
acter of  the  image.     Slide  a  piece  of  cardboard  along  gradu- 
ally between  the  prisms  and  observe  the  changes  in  the  image. 

Try  two  prisms  reversed  in  position,  one  of  them  crown 
glass,  and  the  other  flint. 

555.  Exercise.*  —  Project    a  spectrum  on    the  screen  as 
directed   in  Art.  551.     Between  the  prism  and  screen  hold  a 
large    convex    lens   to   receive  the  spectrum.     Move  the  lens 
along  the  line  of  light,  and  it  will  be  possible  to  find  a  posi- 
tion where    a  white   image    of    the    slit    is   produced   on  the 
screen. 

If  the  spectrum  is  received  on  a  concave  mirror  a  similar 
result  can  be  obtained. 

What  does  this  experiment  prove  the  colored  image  to 
be? 


LIGHT,  317 

556.  Exercise.*  —  Fill    an   air-thermometer   bulb,    4  cm. 
in  diameter,  with  clear  water.     In  front  of  the  porte  ramie  re, 
or    lantern,    place    a   large  white-paper    screen   in  which  is  a 
circular  opening  about  3.75  cm.  in  diameter.     Support  the  bulb 
in  a  clamp  so  that   the   cylindrical   beam  of  light  is  incident 
on  it.     There  will  be  formed  on  the  screen  a  circular  spectrum 
resembling  a  rainbow.     The    distinctness  of  the  bow  will  de- 
pend  on   the  distance  of  the  bulb  from  the  screen,    and   the 
nearness   of   the  bulb  to  a  true  sphere.       With  sunlight  in  a 
very  dark  room  the  secondary  bow  can  be  seen. 

IX.     COLOR. 

557.  Apparatus.  —  Forte  Lumiere,  Colored  Paper,  Prisms, 
Lenses,  Cardboard,  Color-Top,  Colored  Glass,   etc. 

558.  Exercise.  —  Paste  a  strip  of  white  paper  3  cm.  long 
and  '2  mm.  wide  on  a  piece  of  black  cardboard  several  times 
larger.     View    this    whole    strip,    placed    in    a   strong   light, 
through    a    glass    prism,    holding    its    edges    parallel    to    the 
length   of   the    strip.     Examine  in  a  similar  manner  strips  of 
red,  blue,  yellow,  etc.,  paper.     What  color  or  colors  do  you 
find  in  the  light  reflected  by  each  paper? 

559.  Exercise.*  —  Project  the  solar  spectrum  as  directed 
in  Art.  551.     Examine    the    color    of  pieces  of  colored  paper 
when  held    successively  in    the    different    colors  of   the    spec- 
trum.    Explain. 

560.  Exercise.*  —  Place   common  salt  in  the  wick  of  an 
alcohol   lamp    and   analyze  the  light  emitted  by  it  as  in  Art. 
558.     Examine  a  highly  colored   picture  by  its  light  and  ac- 
count for  the  appearance. 


318 


PRACTICAL    PHYSICS. 


PURPL£ 


561.  Exercise.  —  Procure  at  a  toy  store  a  Newton's  color- 
top,  or  any  top  having  a  heavy  metallic  disk.  Cut  out  of 
colored  paper  a  disk  about  10  cm.  in  diameter, 
with  a  small  opening  at  the  centre  of  the 
size  of  the  top-handle.  Slit  them  along  a 
radius  (Fig.  230),  from  circumference  to  FIG.  230. 

centre,  so  that  two  or  more  of  them  can  be  placed  together, 

exposing  any  propor- 
tional part  of  each 
one  as  desired.  Select 
seven  disks  whose 
colors  most  nearly 
represent  those  of  the 
solar  spectrum,  put 
them  together  so  that 
equal  portions  of  the 
colors  are  exposed, 
and  then  place  this 
compound  disk  over 
the  handle  of  the  top 
when  rapidly  rotat- 
ing. Examine  the 


FIG.  231. 


colors  in  a  strong  light. 

Try  violet,  red,  and  green  disks,  exposing 
equal  portions.  Inference.  In  like  manner 
try  red,  green,  and  blue.  Inference. 

Try  two  disks  whose  colors  are  opposite  in 
Fig.  231.  Inference.  Try  any  two  alter- 
nate colors.  Inference.  Ascertain  the  effect 
of  using  unequal  portions.  Try  a  black  disk 
and  a  white  one. 

A  small  whirling  machine,  Fig.  232,  or 
an  electric  motor,  may  be  substituted  for  the  top. 


LIGHT. 


319 


562.  Exercise.*  —  Project  on  the  screen  the  spectrum  of 
the  sun  or  the  electric  light.  By  means  of  a  large  lens  converge 
the  rays  to  a  focus,  producing  a  white  image  of  the  slit  on  the 
screen.  Prepare  two  strips  of  black  cardboard,  in  each  of 
which  is  cut  a  slit  2  mm.  wide  and  2.5  cm.  long,  and  insert 
them  in  a  strip  of  blackened  wood  with  a  groove  cut  in  it  so 
that  the  slits  can  be  adjusted  at  any  desired  distance  apart 
(Fig.  233).  Place  this  screen  between  the  lens  and  the 
prism  and  set  the  slits  so  that  one  color  passes  through 
each  opening.  Observe  the  color  of  the  image  formed  by  the 
lens. 

Ascertain  if  any  two  col- 
ors will  produce  a  white 
image. 

Intercept  one  of  the 
spectrum  colors  by  a  nar- 
row strip  of  cardboard 
held  by  a  clamp  between 
the  prism  and  the  lens,  and 
note  the  color  of  the  image. 

^-j/ 

FIG.  233. 

563.  Exercise.*  — Pro- 
ject a  bright  continuous  spectrum  on  the  screen,  look  steadily 
at  it  for  a  minute,  at  the  end  of  which  time,  without  removing 
the  gaze  from  the  screen,  shut  off  the  light  giving  the  spectrum, 
and  turn  up  the  gaslight  or  lamp.  Observe  the  change  in  the 
image  as  you  continue  to  look  at  the  screen.  Explain. 


564.  Exercise.  —  Lay  a  circular  piece  of  blue  paper,  15 
mm.  in  diameter,  with  a  thread  attached,  on  a  small  sheet  of 
white  or  gray  paper.  Look  steadily  at  the  blue  paper  in  a  strong 


320  PRACTICAL   p/irxivs. 

light  for  15  seconds,  then,  without  moving  the  eye,  suddenly 
pull  away  the  blue  disk,  and  observe  the  color  of  the  after- 
image. Try  other  colors. 

565.  Exercise.*  —  Project  on  a  screen  with  a  lantern,  or 
porte  lumiere,  and  lens  an  image  of  a  round  hole  in  a  piece  of 
cardboard.  Look  steadily  at  the  image  for  25  seconds,  then, 
without  removing  the  eye,  withdraw  the  cardboard,  and  observe 
the  color  of  the  after-image. 

Repeat  the  experiment 
with  the  aperture  covered 
with  red  glass.  Try  glass  of 
other  colors.  Try  the  chemi- 
cal tank  (Fig.  234)  filled 
with  a  solution  of  picric  acid. 
Try  other  colored  solutions. 

FIG  2Mi  566.  Exercise.*— Paste 

an  image  of  an  object  cut 

out  of  opaque  paper  on  a  piece  of  colored  glass  of  the  size  of 
a  lantern  slide.  Project  an  image  of  this  object  on  the  screen, 
gaze  steadily  at  it  for  a  few  moments,  then  suddenly  cut  off  the 
projecting  light,  and  turn  up  the  gas  or  lamp.  Observe  the 
after-image.  Explain. 

X.      SPECTRUM    ANALYSIS. 

567.  Apparatus.  —  Porte    Lumiere,    Prisms,    Spectroscope, 
Platinum    Wire,    Colored    Glass,   Test-Tubes,  etc. 

568.  Exercise.*  —  Proceeding  as  in  Art.  551,  project  the 
solar  spectrum  on*  the  screen,  using  a  very  narrow  slit  and  a 


LIGHT.  321 

carbon  disulphide  prism.  If  the  focusing  is  carefully  done,  and 
the  room  is  quite  dark,  a  number  of  dark  lines  will  be  seen 
crossing  the  spectrum  vertically,  showing  that  the  solar  spec- 
trum is  not  continuous.  Diagram  their  position. 

These  lines  are  easily  seen  by  placing  the  eye  in  the 'pencil  of 
light  diverging  from  the  prism. 

569.  Exercise.  —  Turn  the  slit  of  the  spectroscope  (Fig. 
218)  toward  a  distant  white  building.  Focus  the  telescope,  and 
place  the  prism  at  the  angle  of  least  deviation  for  that  part  of 
the  spectrum  in  the  field.  It  will  be  found  easier  to  study  the 
spectrum  if  the  telescope  tube  is  thrust  through  a  sheet  of  card- 
board to  cut  off  from  the  eye  the  light  not  passing  through  the 
apparatus. 

Make  a  map  of  a  few  of  the  more  prominent  lines,  by  taking 
the  reading  of  the  angular  scale  found  on  the  platform  of  the 
instrument  when  the  intersection  of  the  cross-hairs  is  on  the 
dark  line,  and  laying  it  off  on  one  side  of  a  rectangle,  say  10 
cm.  long,  representing  the  spectrum.  As  the  ends  of  the  rect- 
angle correspond  to  the  readings  given  by  the  angular  scale  of 
the  spectroscope  for  the  limits  of  the  spectrum,  the  number  of 
degrees  corresponding  to  each  centimetre  of  the  rectangle  is 
easily  ascertained, 
and  each  dark  line 
located  by  comput- 
ing how  many  centi- 
metres correspond 
to  the  angular  dis- 
tance the  line  is  from 
the  end  of  the  spec-  FIG  235 

trum. 

As  spectroscopes  are  expensive,  the  student  may  construct 
one  by  observing  the  following  directions  :  — 


322  PRACTICAL    PHYSICS. 

Make  out  of  heavy  pasteboard  a  box  30  cm.  long  (Fig.  235), 
whose  cross-section  is  a  rectangle.  One  of  the  lateral  faces 
should  be  shorter  than  the  opposite  one,  as  shown  in  Fig.  236. 


FIG.  236. 

In  the  oblique  end  cut  a  small  aperture  3  mm.  in  diameter  and 
considerably  nearer  the  shorter  face.  In  the  opposite  end  cut 
a  rectangular  opening  3  cm.  square,  and  cement  over  it  a  slit 
prepared  by  pasting  tin  foil  smoothly  over  a  piece  of  clear 
glass,  and  cutting  a  line  through  the  foil  1.5  cm.  long  by 
drawing  a  knife-edge  across  it.  The  depth  and  width  of  the 
box  will  be  determined  by  the  size  of  the  prism  P.  Paint  the 
inside  of  the  box  a  dead  black,  using  thin  shellac  varnish  and 
lamp-black.  Set  the  prism  in  the  position  shown  in  Fig.  230, 
fastening  it  in  place  by  gluing  blocks  in  the  angles.  The  box 
must  be  provided  with  a  tight-fitting  cover.  The  prism  described 
in  Art.  551  will  show  many  of  the  Fraunhofer  lines  on  direct- 
ing the  slit  S  toward  the  bright  sky  and  holding  the  eye  close 
to  the  opening  E,  looking  in  a  line  perpendicular  to  that  face. 

570.  Exercise.*  —  Take  a  piece  of  platinum  wire  of  about 
the  diameter  of  a  fine  sewing-needle  ;  bend  the  end  into  a  small 
loop  about  2  mm.  in  diameter ;  fuse  a  small  bead  of  the  salt  to 
be  experimented  with  into  the  loop,  and  fasten  the  wire  in  a 
clamp  so  that  the  bead  is  brought  into  the  front  edge  of  a  gas 
or  alcohol  flame  at  a  point  a  little  below  the  slit  of  the  spectro- 


LIGHT.  323 

scope.  On  looking  through  the  telescope  a  bright-line  spectrum 
will  be  seen.  Examine  in  this  way  the  spectra  of  the  following 
substances,  mapping  the  more  prominent  lines  as  directed  in 
Art.  569  :  A  salt  of  lithium,  potassium,  sodium,  strontium, 
barium,  etc.  Search  for  Fraunhofer  lines  occupying  the  same 
positions  as  these  bright  ones. 

571.  Exercise.*  —  Direct    the   slit    of    the    spectroscope 
toward    the  electric  light.     Place  close   to    the    slit  a  Bunsen 
flame,  and  hold  in  it  a  pellet  of  sodium.     Mark  the  position 
of    the    dark    line    crossing  the  spectrum.     Now  shut  off  the 
electric  light,    and    a    bright  line  will   be  seen  occupying  the 
place  of  the  dark  one.     Explain. 

572.  Exercise.* —  Observe  the  spectrum  of  sunlight  when 
blue  glass  is  placed  over  the  slit  of  the  spectroscope.    Try  glass 
of  some  other  color.     Ascertain  the  effect  of  superposing  two 
or    more   pieces.     Try  a  test-tube   filled  with    an    ammoniacal 
solution  of  copper  sulphate.       Try,  successively,  solutions*  of 
picric    acid,    quinine,    etc.      Compare    the    spectrum  with   the 
color  of  the  substance. 

573.  Exercise.  —  Place    before    the   slit   of   the  spectro- 
scope a  test-tube  containing  a  few  clippings  of  copper.    Pour 
on    the    copper    a    few  drops    of    nitric    acid,    and  study  the 
spectrum    of    sunlight    after    passing    through     the     reddish- 
brown  gas  '    which  will  now  fill  the  tube. 

574.  Exercise.*  —  Support  before  the  slit  of  the  spectro- 
scope   a    Geissler's    tube    charged  with  some  known  gas,   and 
observe  the  spectrum  on  illuminating  the  tube  with  an  induc- 
tion coil. 

1  After  chemical  action  has  stopped,  cork  the  tube  to  prevent  the  fumes  from  escap 
intf  and  corroding  the  metallic  parts  of  the  spectroscope. 


324  PRACTICAL    PHYSICS. 


XI.     INTERFERENCE    OF    LIGHT. 

575.  Apparatus.  —  Porte    Lumiere,     Thick     Glass,     Iron 
Clamp,     Window-Glass,     India-Ink,     Lenses,      Nobert      Grating, 
Perforated     Cardboard,     Mother-of- Pearl,     etc. 

576.  Exercise.*  —  Procure    two    square    pieces   of  heavy 
plate  glass,  about  8  cm.  on  an  edge.     Clean-  them  thoroughly, 
then  press  them  gently  together  by  means  of  common  spring 
clothes-pins  on  three  of  the  corners,  and  the  supporting  clamp 
at  the    fourth   corner.       Let  a  beam   of    sunlight   be  incident 
on    the    surface    at    an    angle    of  45°.     In  the  reflected  beam 
place  a  lens,  and  project  an  image  of  the  porte-lumiere  open- 
ing  on    the    screen.      .Notice  the  colors   on  the  image  as  the 
pressure  at  the  clamp  is  changed.     Explain. 

Beautiful  colors  are  seen  if  two  such  pieces  of  glass  are 
firmly  pressed  together  at  their  centres  by  means  of  a  small 
iron  clamp. 

577.  Exercise.*  —  Make  out  of    coarse  iron  wire   a  ring 
8  cm.  in  diameter,  soldering  it  to  a  wire  for  a  handle.     Dip 
the  ring  into  a  soap  solution  prepared  as  directed  in  Art.  80, 
and  support  it  in  the  beam  of  light  in  the  place  of  the  glass 
plates    in    the   last   experiment.     Observe   the    play  of   colors 
across  the  image  on  the  screen. 

Observe  the  phenomenon  when  one-colored  light  is  employed. 

578.  Exercise.  —  Paint  one    side   of  a  strip   of  window- 
glass  with  India-ink,    rendering  it   opaque.     When  dry,  rule, 
with  a  fine    needle,    a   number   of    parallel  lines,  as  close  to- 
gether   as    possible,    by  cutting    through  the  ink  to  the  glass. 


LIGHT.  325 

Now  stand  about  5  m.  away  from  a  lighted  lamp  and  view  it 
through  this  grating.     P^xplain. 

View  through    this   grating  a  slit   placed   across   the   porte 
lumiere. 

579.  Exercise.* —  Project  with  a  lens   an  image  of  a  slit 
placed  across  the  porte  lumiere,  having  the  room  as  dark  as 
possible.     Over  the  slit  place  a  Nobert  grating  with  its  lines 
parallel  to  the  slit.     Observe  the  series  of  spectra.     Compare 
the    relative    spaces   occupied   by  the  colors  with  the  relative 
spaces  when  the  spectrum  is  obtained  by  a  prism. 

Photographs  of  these  gratings  are  nearly  as  efficient  as  the 
originals,  and  cost  only  about  one-fourth  as  much. 

580.  Exercise.*  —  Reduce  the  opening  in  the  porte  lumiere 
to  a  circular  hole  2.5  cm.  in  diameter.      Cover  this  aperture 
with    a   piece    of   perforated   cardboard,    and    project  with    a 
lens   an   image    of   it  on  the  screen.     Try  two  pieces,  slowly 
sliding  one  over  the  other.     Explain. 

581.  Exercise.*  —  Substitute  for  the  glass  plates  in  Art. 
576  a  piece  of  mother-of-pearl,  and  place  a  slit  in  the  open- 
ing of  the  porte  lumiere.     A  peculiarly  colored  image  should 
be  obtained.      Now  substitute  for  the  pearl  an  impression  of 
it  taken  in  black  sealing-wax.     Explain. 

XII.     OPTICAL,    INSTRUMENTS. 

582.  Apparatus.  —  Florence    Flask,     Lenses,     Cardboard 
Telescope,    etc. 

583.  Exercise.*  —  Fill  a  £-litre  globular  flask  with  dis- 
tilled   water  to  represent  the  eyeball.     Cover  one-half  of  the 


326 


PRACTICAL    PHYSICS. 


globe  with  black  paper,  with  a  round  hole  cut  in  it.  This  will 
represent  the  iris  and  pupil.  Place  a  convex  lens  of  long  focal 
distance  in  front  of  this  hole  to  represent  the  cornea  and  the 
crystalline  lens  combined.  Support  a  lighted  candle  in  front 
of  this  hole,  and  at  such  a  distance  as  to  form  a  clear  image  on 
a  paper  screen  placed  behind  the  globe.  Now  move  the  candle 
toward  the  globe  till  the  image  is  quite  indistinct,  and  then  en- 
deavor to  restore  the  distinctness  of  the  image  by  interposing  a 
second  convex  lens.  Also  move  the  candle  away  from  the 
globe,  and  restore  the  distinctness  of  the  image  by  interposing 
a  concave  lens.  What  defects  of  the  eye  are  illustrated  in 
these  experiments? 


584.  Exercise.*  —  The  principle  of  the  microscope  may 
be  illustrated  as  follows  :  Select  two  convex  lenses  of  the  focal 
distances  3  and  5  cm.  respectively.  Mount  them  carefully 
in  cork  or  wooden  rings,  as  shown  in  Fig.  237,  cutting  a 

small  portion  from  one 
edge  to  produce  a  flat 
surface.  Glue  these 
|p  mounted  lenses  on  a 
small  board  15  cm. 
long  by  3  cm.  wide, 
placing  the  one  of 
longer  focus  at  the 
end  A,  to  serve  as  the 
eye-glass,  and  the  other  distant  from  it  11  cm.,  as  at  C,  to 
serve  as  object-glass.  Cut  two  cork  disks,  B  and  D  ;  insert 
into  one  of  them  a  rectangular  piece  of  stiff  writing-paper,  and 
into  the  other  a  similar  piece  of  thin  sheet-brass.  Slightly  oil 
the  paper  to  render  it  translucent,  and  drill  in  the  brass  plate 
a  number  of  small  holes,  arranged  in  the  form  of  a  cross,  at 


FIG.  237 


LIGHT. 


327 


the  height  of  the  centre  of  the  lens  above  the  base.  Before 
placing  the  brass  plate  D  in  position,  place  the  paper  screen 
B  about  4  cm.  from  the  lens  A,  and  move  it  to  and  fro  till  a 
position  of  distinct  vision  is  found  for  it  when  viewed  through 
A.  Now  place  a  flame  at  the  other  end  of  the  board,  exactly 
in  line  with  the  centre  of  the  lenses,  and  between  it  and  C  place 
the  brass  plate  D,  distant  from  C  about  17.5  mm.  Move  1) 
till  a  distinct  image  of  the  cross  is  formed  on  B  ;  then  a  magni- 
fied image  of  the  cross  will  be  seen  through  A,  but  more  clearly 
defined  if  B  is  removed.  What  is  the  office  of  each  lens? 

To  determine  the  magnifying-power  ascertain,  as  in  Art. 
549,  the  magnifying-power  of  the  eye-piece  and  object-glass 
separately,  and  obtain  their  product. 


585.  Exercise.  —  The  principle  of  the  telescope  may  be 
illustrated  as  follows  :  Mount  two  convex  lenses  as  directed  in 
the  last  article,  having  the  focal  distances  30  cm.  and  5  cm. 
respectively.  Cement  the  larger  one,  A,  to  one  end  of  a  board 
50  cm.  long  by  10  cm.  wide  (Fig.  238),  and  the  other,  B,  to  a 
second  board  5 
cm.  square,  but  of 
such  a  thickness 
as  to  bring  the 
centres  of  the 
lenses  in  a  line 
parallel  to  the 
large  board  when 
the  small  board 

rests  upon  it.  Prepare  a  translucent  screen  as  in  the  last 
article.  Place  the  apparatus  on  one  end  of  a  long  table,  with 
the  lens  A  directed  toward  a  candle-flame  at  the  other  end.  Set 
the  screen  to  receive  the  image  of  the  candle  formed  by  A ; 


FIG.  238. 


328 


PRACTICAL    PHYSICS. 


then  by  moving  the  eye-piece  B,  a  place  will  be  found,  giving 
an  enlarged  image  of  this  image  on  the  translucent  screen,  and 
a  brighter  image  of  the  candle  on  removing  the  screen.  What 
is  the  office  of  each  lens  ? 

If  the  eye-piece  is  made  of  two  lenses,  b  and  c  (Fig.  239), 

b  having  a  focal  distance  of  f> 
cm.  and  c  of  3  cm.,  the  distance 
between  them  being  9  cm.  ;  on 
placing  the  screen  between  b  and 
c,  an  erect  image  of  the  candle  will 
be  obtained  instead  of  an  inverted 
one  as  before,  and  on  looking 
through  b  an  erect  and  magnified 
image  of  the  candle  will  be  seen. 
What  is  the  office  of  the  lens  c? 


FIG.  239. 


586.  Exercise.*  —  The  principle  of  the  Galilean  tele- 
scope may  be  illustrated  as  follows  :  Substitute  for  the  lens  B 
in  the  last  experiment  a  concave  lens  of  5  cm.,  focal  length. 
Distinct  vision  will  be  secured  on  placing  B  between  the  screen 
and  the  lens  A. 


587.  Exercise.  —  Determine  the  magnif ying-power  of  a 
telescope. 

Direct  it  toward  the  open  sky,  and  there  will  be  seen  near  the 
eye-piece,  and  a  little  beyond  it,  a  small  illuminated  circle. 
This  is  an  image  of  the  objective  opening  of  the  telescope. 
Measure  the  diameter  of  this  image,  employing  a  finely  divided 
scale.  The  magnifying-power  is  equal  to  the  quotient  of  the 
diameter  of  the  object-glass  by  that  of  this  illuminated  circle. 


LIGHT.  329 


XIII.      DOUBLE     REFRACTION     AND     POLARIZATION     OF 

LIGHT. 

588.  Apparatus.  —  Iceland      Spar     Crystal,     Tourmaline 
Tongs,    Polariscope,    Lenses,    etc. 

589.  Exercise.  —  Place  a  crystal  of  Iceland  spar  over  a 
small  dot  on   a  white   sheet   of    paper,   and   observe    the    dot 
through   it.       Rotate  the  crystal  about  an  axis    perpendicular 
to  the  paper,  and  notice  the  behavior  of  the  images  of  the  dot. 
Mark  the  relative  brightness  of  these  images  while  the  crystal 
rotates  as  you  view  them  through  a  tourmaline  plate  or  Nicol 
prism. 

590.  Exercise. —  Procure  a  pair  of  tourmaline  tongs,  an 
instrument  consisting  of  two  thin  plates  cut  from  the  tourma- 
line crystal  and  mounted  as  shown  in 

Fig.  240.  Look  through  the  plates 
at  the  bright  sky  and  observe  the 
changes  in  brightness  as  one  plate  is  FIG  94u 

turned  on  an  axis  within  the  support- 
ing ring. 

Set  the  plates  so  that  the  view  is  darkest,  then  place  between 
them  a  quartz  spectacle-lens,  known  as  a  pebble-lens,  compar- 
ing the  effect  with  that  produced  by  a  glass  lens. 

Opticians  prepare  thin  plates  of  crystalline  substances,  such 
as  Iceland  spar,  quartz,  arragonite,  etc.  Place  any  of  these 
you  may  be  able  to  procure  between  the  plates  of  the  tongs 
and  observe  the  peculiar  figures  and  the  play  of  colors  as  one 
of  the  plates  is  rotated. 

591.  Exercise.  —  Examine  with  a  polariscope  pieces  of  un- 
annealed   glass,    as    glass    stoppers,   paper   weights,    Rupert's 


330  PRACTICAL     1>UYHI(!H.     . 

drops,  etc.  ;  also  thin  plates  of  mica,  selenite,  quartz,  Iceland 
spar,  etc. 

An  efficient  polariscope  may  be  constructed  as  follows :  Cut 
a  rectangular  piece  of  board  36  cm.  long,  10  cm.  wide,  and  2.5 
cm.  thick,  and  also  a  right  triangular  one,  having  the  sides 
about  the  right  angle  24.5  cm.  and  17.4  cm.  respectively. 

Fasten  these  pieces  to- 
gether as  shown  in  Fig. 
241,  the  shorter  side 
about  the  right  angle 
being  the  vertical  one. 
At  A,  5  mm.  from  the 
end  of  the  board,  cut 

"  t-» 

FlG  241  a    groove    to   support  a 

plate   of    ground    glass, 

H,  10  cm.  square.  Between  H  and  B  place  three  or  four 
pieces  of  thin  plate  glass,  each  10  cm.  square,  on  a  piece 
of  dead-black  paper  to  serve  as  a  polarizer.  At  E,  4  cm. 
from  B,  support  in  a  transverse  groove  perpendicular  to  the 
plane  of  BD,  a  glass  plate,  to  serve  as  a  shelf  for  supporting  the 
objects  under  examination.  At  D  glue  a  wooden  block  5  cm. 
high,  and  2.5  cm.  thick,  having  an  aperture  through  its  centre 
2.5  cm.  in  diameter,  parallel  to  the  surface  of  the  plane,  to 
support  the  analyzer.  This  analyzer  may  be  constructed  in 
either  of  two  ways  :  first,  by  procuring  from  an  optician  a  small 
Nicol  prism,  and  mounting  it  in  a  centrally  apertured  cork 
inserted  in  a  paper  or  brass  tube,  2.5  cm.  in  diameter  (Fig.  242, 
A)  ;  or,  secondly,  by  procuring  a  paper  or  metal  tube  as  before, 
fitting  to  it  an  inner  tube  of  pasteboard  divided  obliquely  (Fig. 
242,  C),  at  an  angle  of  35°  25'  with  the  axis  of  the  tube, 
and  placing  between  these  two  parts  12  or  15  elliptical  micro- 
scope cover-glasses,  shown  in  section  in  Fig.  242,  B.  In  either 


LIGHT. 


331 


' 


B 


Fiu.  24-2. 


case  one  end  of  the  tube  is  capped,  and  in  the  cap  is  a  central 
opening  2  mm.  in  diameter.  A  shoulder  is  provided  for  the 
tube  by  gluing  on  the  outside  a  paper  ring. 

In  using  the  instrument  let  light  from  the  bright  sky  pass 
through  H,  and  be  incident  on  K,  by  which  it  is  reflected  through 
the  object  on  E, 
to  the  analyzer  F. 
On  rotating  F  on 
its  axis ,  a  fine  play 
of  colors  will  be 
seen  on  the  ob- 
ject, due  to  inter- 
ference. 

A  very  convenient  instrument  for  investigations  in  polari- 
zation is  Norrernberg's  doubler,  a  simple  form  of  which  may  be 
constructed  as  follows :  Knock  out  the  opposite  sides,  EL  and 
PM,  of  a  large  cigar-box,  and  on  the  other  two  lateral  faces  fix 

guides  for  the  polarizing  plate  B 
(Fig.  243),  so  that  the  plate  makes 
an  angle  of  35°  25'  with  the  edge  EF. 
On  the  end  FM  lay  a  piece  of  good 
looking-glass  the  size  of  the  end  ;  and 
in  the  other  end  cut  a  hole,  in  which 
the  analyzer  A,  either  a  Nicol  prism 
or  a  bunch  of  glass  plates,  can  be  ro- 
tated. The  objects  under  exami- 
nation are  placed  on  the  looking- 
glass.  The  light  incident  on  B  is 
reflected  to  D  and  partially  polarized  ; 
D  in  turn  reflects  it  through  A  to  the  eye.  If  desired,  a  hori- 
zontal shelf  between  B  and  A  could  be  put  in,  having  a  circular 
opening  for  the  passage  of  light.  Objects  could  then  be  ex- 
amined resting  on  this  shelf  over  the  opening. 


FIG.  243. 


332 


PEA CTICAL     I'll ) rSI(  '8. 


592.  Exercise.  —  Procure  several  strips  of  glass,  such  as 
are  used  in  preparing  microscope  slides.  Form  on  the  centre  of 
each  a  paraffine  ring  2  cm.  in  diameter.  Support  the  glass  in 
a  horizontal  position,  and  put  within  the  circle  a  few  drops  of 
a  solution  of  some  chemical  salt,  and  let  it  remain  undisturbed 
until  crystals  are  formed.  Examine  these  under  a  microscope 
with  a  polarizing  attachment.  The  following  list  of  salts  is  rec- 
ommended :  Alum,  potassium  bichromate,  mercury  bichloride, 
boracic  acid,  potassium  carbonate,  citric  acid,  potassium  chlo- 
rate, potassium  iodide,  ammonium  nitrate,  copper  sulphate,  iron 
sulphate,  potassium  sulphate,  potassium  ferrocyanide,  etc. 

An  instrument  suitable  for  examining  such  crystals  can  be 
constructed  as  follows  :  Construct  an  analyzer  as  directed  in 
the  last  article,  and  fit  it  in  the  draw-tube 
of  a  compound  microscope  (Fig.  244),  be- 
tween the  eye-piece  and  the  object-glass. 
A  similarly  constructed  tube  must  be  made 
for  a  polarizer,  and  fitted  to  a  second  tube 
somewhat  shorter,  turning  freely  within  it 
without  falling  out.  Cement  this  outer  tube 
to  the  under  side  of  the  microscope  stage 
with  the  axis  of  the  tube  exactly  in  that  of 
the  draw-tube  above,  but  leaving  the  inner 
tube  free  to  turn  on  its  axis.  Very  satisfac- 
tory results  can  be  obtained  from  the  com- 
mon draw-tube  microscopes,  and  even  the 
simple  botanizing  glass  can  be  easily  adapted 
to  exhibit  the  phenomena  of  polarized  light 
(see  "The  Scientific  American"  for  July  31,  1886).  Paper 
tubes  to  fit  the  tubes  of  the  microscope  are  easily  made  by 
gumming,  writing-paper,  and  winding  it  around  a  cylinder  of 
the  proper  size. 


FIG.  244. 


LIGHT.  333 

593.  Exercise.  —  Dissolve  salicine  in  one  part  alcohol  to 
four  parts  water,  made  rather  hot,  obtaining  a  saturated  solu- 
tion. Pour  a  layer  on  a  microscope  slide,  and  evaporate 
quickly  with  rather  a  strong  heat.  Examine  the  crystals 
obtained  under  the  microscope  with  the  polariscope  attach- 
ment. 


APPENDICES. 


APPENDICES. 


APPENDIX  A. 
THE      PHYSICAL      LABORATORY. 

594.  The  Room.  —  Where  a  separate  room  can  be  pro- 
vided for  experimental  work  in  Physics,  it  should  be  large,  well 
ventilated,  and  have  a  southern  exposure.  Opening  off  from  it 
should  be  a  room  for  the  storage  of  apparatus.  Provision 
should  be  made  for  darkening  the  windows,  either  by  inside 
blinds  or  opaque  curtains  mounted  on  spring  rollers.  If  cur- 
tains are  used,  the  lateral  edges  must  slide  in  deep  grooves, 
made  by  nailing  strips  on  the  casing,  to  prevent  the  light  from 
entering  the  room  around  the  edges. 

A  few  heavy  flat-top  tables,  about  32  in.  high,  3  ft.  wide, 
and  of  such  length  as  the  room  permits,  should  be  obtained. 
These  tables  should  have  no  iron  in  their  structure,  and  to  make 
it  possible  to  clamp  apparatus  on  them  the  top  should  pro- 
ject at  least  four  inches  beyond  the  frame.  In  a  part  of  the 
room  where  there  is  a  good  light,  place  a  carpenter's  work- 
bench, with  a  vise  and  anvil  upon  it.  Above  it,  on  the  wall, 
fasten  a  cupboard,  to  contain  such  tools  as  saws,  planes, 
brace  and  bits,  drills,  hammer,  chisels,  try-square,  flies,  wire- 
cutter,  soldering-iron,  oil-stone,  nails,  screws,  both  iron  and 
brass,  tacks,  etc.  This  part  of  the  equipment  should  not  be 
overlooked.  School  authorities  will  seldom  refuse  to  appro- 
priate money  to  be  spent  in  this  way. 

A  side-table  for  the  few  chemicals  needed  will  be  found  con- 
venient. A  sink  for  waste  water  must  by  no  means  be  omitted. 


338  PRACTICAL    PHYSICS. 

Connect  the  room  with  the  water  system  if  there  is  one ;  if  not, 
place  a  galvanized  iron  tank  at  one  end  of  the  sink,  having  a 
capacity  of  two  or  three  barrels,  to  be  filled  with  water  from 
the  well  or  cistern  by  means  of  a  force-pump. 

As  soon  as  possible  put  a  well- filled  bookcase  in  the  room, 
with  a  table  and  chairs  near  by,  where  students  may  look  up 
points  regarding  their  work.  Such  books  as  the  following  are 
recommended :  — 

Ganot's  Physics,  by  Atkinson  ;  Practical  Physics,  by  Guthrie  ; 
Cooke's  Chemical  Physics  ;  Elementary  Practical  Physics,  by 
Stewart  and  Gee  ;  Practical  Physics,  by  Glazebrook  and  Shaw  ; 
Physical  Manipulations,  by  Pickering ;  Experimental  Physics, 
by  Weinhold ;  Physical  Constants,  by  Everett ;  The  Art  of 
Projecting,  by  Dolbear ;  Light,  by  Wright ;  Light,  by  Mayer 
and  Barnard  ;  Sound,  by  Mayer  ;  Sound,  by  Tyndall ;  Magnet- 
ism and  Electricity,  by  Guthrie  ;  Electrical  Rules  and  Tables, 
by  Munro  and  Jamieson ;  Fleming's  Short  Lectures  to  Elec- 
trical Artisans  ;  Practical  Mechanics,  by  Perry  ;  Physical  Meas- 
urements, by  Kohlrausch ;  Practical  Electricity,  by  Ayrton ; 
Handbook  of  Electrical  Testing,  by  Kempe. 

The  walls  of  the  room  would  look  more  attractive  if  they 
were  decorated  with  the  pictures  of  prominent  scientific  men. 
Bare  walls  are  not  very  inspiring ;  good  work  is  not  wholly  in- 
dependent of  the  student's  surroundings.  Charts  of  spectra 
neatly  framed  would  be  both  useful  and  ornamental. 

If  illuminating  gas  is  procurable,  by  all  means  introduce  it 
into  the  laboratory,  supplying  each  table  with  jets  suspended 
from  the  ceiling,  making  connections  with  them  by  rubber 
tubing.  The  advantage  of  this  method  is  that  the  tables  can 
be  moved  about  if  necessary ;  there  is  no  iron  beneath  them  to 
interfere  with  the  action  of  magnetic  needles,  and  when  the  gas 
is  not  in  use  the  fixtures  are  out  of  the  way. 


THE    PHYSICAL    LABORATORY.  339 

It  is  not  to  be  expected  that  every  luxury,  or  even  every  con- 
venience, can  be  provided  at  the  outset.  Let  the  essentials  be 
secured,  and  then  add  from  time  to  time  such  fixtures  as  will 
enable  the  work  to  be  done  with  greater  accuracy  and  at  less 
inconvenience. 

If  the  recitation-room  is  large,  and  the  class  small,  the  back 
part  of  the  room  might  be  fitted  up  for  experimental  work. 
This  would  be  much  better  than  the  entire  omission  of  this  im- 
portant kind  of  training.  The  days  of  teaching  science  at  long 
range,  as  it  were,  are  passed.  That  the  pupil  must  come  in 
actual  contact  with  the  phenomena  to  be  studied  is  recognized 
by  every  wide-awake  instructor.  The  apparatus  should  be  put 
in  his  hands,  with  clear  directions  regarding  its  use ;  in  this 
way  there  are  trained  all  of  the  powers  of  the  mind,  the  obser- 
vational not  the  least  important.1  Faraday  used  to  affirm  that 
he  always  wished  to  perform  experiments  himself  ;  that  he 
always  learned  something  in  doing  the  work  that  the  descrip- 
tion in  words  could  not  convey  to  him.  An  experiment  which 
fails  is  often  more  instructive  than  one  which  succeeds.  In 
finding  the  cause  of  failure  more  will  often  be  learned  than 
when  the  work  goes  through,  as  if  by  routine. 

595.  Apparatus.  —  It  is  a  mistake  to  suppose  that  elabo- 
rate and  highly  finished  apparatus  is  necessary  for  successfully 
prosecuting  experimental  work  in  Physics.  Neither  should  it 
be  expected  that  all  the  required  appliances  for  the  complete 
investigation  of  every  department  of  the  subject  can  be  pro- 


1 A  few  experiments  performed  by  himself  will  give  the  student  a  more  intelligent 
interest  in  the  subject,  and  will  givo  him  a  more  lively  faith  in  the  exactness  and  unifor- 
mity of  nature,  and  in  the  inaccuracy  and  uncertainty  of  our  observations,  than  any 
reading  of  books,  or  even  witnessing  elaborate  experiments  performed  by  professed 
men  of  science.  J.  CLERK  MAXWELL. 


840  PRACTICAL    PHYSICS. 

vided  at  the  outset.  Let  some  of  the  more  important  pieces  be 
secured,  selecting  them  with  the  view  of  adding  the  others  as 
soon  as  practicable.  In  this  way  an  outfit  will  be  obtained 
in  time,  where  each  piece  has  its  place  and  all  fit  harmoniously 
together.  Much  can  be  done  with  a  few  wisely  chosen  pieces. 
Although  the  author  does  not  believe  that  giving  instruction  in 
physical  technics  is  the  proper  work  of  the  laboratory,  yet  he 
would  permit  a  limited  amount  of  apparatus  construction,  if  too 
much  time  is  not  consumed  in  it.  Each  class  will  usually  have 
its  handy  boy,  whose  mechanical  gifts  can  be  turned  to  good 
account  by  having  him  construct,  now  and  then,  a  desirable 
piece  of  apparatus.  The  school  janitor  is  generally  a  man  of 
some  mechanical  skill,  and  will  willingly  construct  frames, 
supports,  and  the  like.  A  small  fee  levied  each  term,  to  cover 
incidentals,  will  always  be  cheerfully  paid  by  the  patrons  of  the 
school,  and  in  the  course  of  the  year  will  amount  to  a  handsome 
sum,  to  be  devoted  to  improving  the  equipment. 

Among  the  first  things  to  be  purchased  are  appliances  for 
measuring  Metre  sticks  can  be  procured  of  the  Metric  Bureau 
for  25  cents  each ;  several  of  these  should  be  obtained.  For 
measuring  small  linear  quantities,  where  a  selection  from  the 
instruments  described  in  the  first  chapter  has  to  be  made,  it  is 
recommended  that  the  Dividers,  Diagonal  Scale,  and  Micrometer 
Caliper  be  chosen,^  and  that  several  of  each  of  the  first  two  be 
purchased.  The  Circular  Protractor  will  be  needed  for  angular 
measurements.  Cheap  and  efficient  ones  are  now  made  of 
horn. 

Good  reliable  Balances  are  indispensable  to  every  laboratory, 
but  unfortunately  they  are  expensive.  The  Jolly  Balance  can 
be  constructed  by  any  one  at  all  skilful  with  tools,  and  makes  a 
very  good  substitute  for  the  beam  balance,  provided  accurate 
weights  are  used.  If  a  support  is  fitted  to  the  Jeweller's  Hand 


,     THE    PHYSICAL    LABORATORY.  341 

Balance,  a  good  deal  of  work  can  be  accomplished  with  it,  if 
one  is  very  careful.  Balances  sensitive  to  a  centigramme  can  be 
imported,  duty  free  for  schools,  from  Germany  for  about  $6.50. 
With  one  set  of  Accurate  Weights  for  comparison,  cheap  ones  can 
be  adjusted,  and,  in  fact,  it  is  not  a  difficult  matter  to  make 
weights  out  of  sheet-brass,  brass  wire,  and  aluminum  wire. 

Of  Glass  Tubing  there  should  be  a  liberal  supply  of  both  large 
and  small  sizes.  Select  tubes  having  thick  walls,  as  they  are 
stronger,  and  bend  without  collapsing.  Rubber  Tubing  for  con- 
nections, and  for  many  other  purposes  described  in  the  preced- 
ing pages,  is  one  of  the  necessities. 

A  few  shillings  appropriated  for  wire,  brass,  copper,  and  iron, 
of  various  diameters,  will  well  repay.  For  electrical  work 
covered  copper  wire  will  be  required  ;  the  desirable  numbers  are 
indicated  in  the  chapter  on  electricity. 

In  constructing  supports  and  many  simple  devices,  there  will 
be  frequent  use  for  ivell-seasoned  pine  lumber  of  different  thick- 
nesses. Material  of  this  kind  should  be  always  on  hand. 

If  gas  is  available,  the  best  lamp  for  heating  purposes  is  the 
Bunsen  Burner  (Fig.  245),  as  it  gives  a  very  hot  and  smokeless 
flame.     In  using  the  burner  care  should  be  taken  to  regulate 
properly  the  supply  of  air  through  the  holes  near 
the  base,  for  if  too  much  air  is  admitted,  the  flame 
is  likely  to  strike  down  the  tube  and  burn  at  the 
lower  part,  giving   a   smoky  flame,  the  heat  of 
which  is  expended,  in  a  measure,  on  the  tube. 
When  gas  is  not  available,  resort  must  be  had  to 
the  alcohol  lamp,  or  to  some   form   of  gasoline 
burner.     An  alcohol   lamp  can  be  extemporized 
out  of  a  bottle,  to  which  is  fitted  a  perforated 
cork,    through  which    passes   some   candle-wick. 
The  top  of  the  cork  can  be  protected  from  the  flame  by  a  layer 


342 


PRACTICAL    PHY8ICS. 


FIG.  246. 


FIG.  247. 


of  plaster-of -Paris.  In  Fig.  246  is  shown  the  Mouth  Blow- 
pipe, an  instrument  easily  made  from  two  pieces  of  glass  tubing 
and  a  sound  cork.  When  great  heat  is  required,  as 
jn  manipulating  heavy  glass  tubing,  resort  must 
be  had  to  the  Blast  Lamp  (Fig. 
247) .  Fig.  248  shows  a  very  con- 
venient form  of  Blower  for  supply- 
ing air  to  the  blast  lamp. 

Fig.  249  represents  the  Florence 
Flask.  The  laboratory  should  be 
supplied  with  several  of  these, 
varying  in  size  from  a  half -litre 
to  a  litre  and  a  half.  When  heat 
is  to  be  applied  to  one,  place  it 
in  a  sheet-iron  shallow  saucer,  containing  fine  sand,  or  a  square 

of  asbestos  paper,  supported 
on  a  ring  of  the  iron  stand  (Fig. 
262),  to  secure  a  uniform  dis- 
tribution of  heat. 
The  Glass  Re- 
tort (Fig.  250) 
may  often  take 
the  place  of  the 
flask,  especially 
when  any  dis- 
tillation is  to  be 
done.  Fig.  251 

exhibits  a  very  useful  form  of  Condenser.  A  large  bottle  or 
flask  may  usually  be  used  as  a  substitute.  Funnels  (Fig.  252) 
are  almost  indispensable.  They  may  be  of  either  glass  or  tin. 
One  form  is  provided  with  a  stop-cock.  The  Graduate  (Fig.  253) 
is  employed  for  the  volume  measurement  of  liquids.  These 


FIG.  248. 


FIG.  249. 


THE    PHYSICAL    LABOEATOEY. 


343 


FIG.  250. 


FIG.  251. 


instruments  should  be  graduated  in  both  the  English  ard  the 
metric  system.  At  least  two  sizes  will  be  desirable,  one  having 
a  capacity  of  25  ccm.  and  graduated  to 
centimetres,  and  a  second  one  holding 
at  least  500  ccm.  The  Cylindrical  Grad- 
uate (Fig.  254)  can- 
not well  be  dispensed 
with,  being  almost 
a  necessity  in  deter- 
mining the  volume  of  irregular  solids  by  the 
displacement  of  water.  These  should  be 
graduated  to  cubic  centimetres.  Two  or  three  of  these  should 

find   a   place  in  the  laboratory,  and 

may  be  used  in  place  of  the  conical 

form.     Fig.   255  shows  the   Pipette- 

Tube,    and 

the  manner 

of     using 

it.    A  glass 

tube,  drawn 

out  a  little 

at  one  end  to  narrow  the  opening, 
makes  an  excellent  substitute.  Beakers 
(Fig.  256)  are  to  be  had  of  various 
sizes  and  shapes.  A  few  holding  a 
litre,  and  several  of  less  volume 
should  be  provided.  Copper  beakers 
are  very  desirable,  as  there  is  no 
danger  of  breaking  them  by  sudden 
changes  of  temperature.  The  first  outlay  is  somewhat  greater, 
but  it  pays  in  the  end  to  procure  them.  A  dozen,  at  least,  of 
large  Test- Tubes  will  be  needed,  and  two  or  three  times  as  many 


FIG.  252. 


344 


PRACTICAL    PHYSICS. 


FIG.  25 1. 


of  smaller  size  (Fig.  257).  To  clean  them,  a  specially  con- 
structed brush  (Fig.  258)  is  recommended. 

It  is  frequently  desirable  to  reduce 
a  substance  to  a  fine  powder.     In  that 
case  a  Mortar  and  Pestle   (Fig.  259) 
is  necessary.    If 
the  substance  to 
be    powdered  is> 
not  very  hard,  a 
stout  bowl  might 
be   used  with  a 
pestle  made  out 
of    hardwood. 
Very  hard    sub- 
sStances  must  be 

broken  with  a  hammer  or  in  an  iron 
mortar.  For  condensing  solutions  or  dry- 
ing substances 
use  an  Evapo- 
rating Dish  (Fig. 

260).  They  are  made  of  either  glass 
or  porcelain.  Common  white  stone- 
ware saucers  are  an  excellent  substi- 
tute, and  are  quite  inexpensive.  In 
heating  them,  the  temperature  must  be 
increased  gradually,  and  they  should 
never  be  exposed  to  the  naked  flame, 
but  should  be  set  in  a  dish  of  sand  and 
kept  at  a  moderate  heat.  Where 

there  is  danger  of  overheating  during  evaporation,  or  where 
it  is  necessary  to  keep  a  substance  at  a  constant  moderate 
temperature,  the  Water-Bath  (Fig.  201)  is  recommended.  This 


Fie.  255. 


FIG.  256. 


THE    PHYSICAL    LABORATORY. 


345 


is  only  a  copper  basin  provided  with  several  rings  of  different 
sizes,  that  the  top  may  be  adjusted  to  the  dish  to  be  placed 
upon  it. 

Figs.  262  and  263  illustrate  the  Iron  Stand 
and  the  Universal  Holder ,  respectively.,  Each 
student,  or  set  of  students,  working  together, 
ought  to  be  supplied  with  one  of  each,  and 


FIG.  258. 

occasionally  more  than  one  of  the  latter  will 
be  found  convenient.  The  price  of  the  iron 
stand  varies  with  the  number  of  rings  supplied 
with  it.  For  most  work  the  single  ring  will  be 
sufficient.  The  universal  holder  can  be  made 
by  any  good  mechanic,  and  in  this  way  secured 
at  a  price  within  reach.  The  Burette  holder  differs  from 


FIG.  257. 


FIG.  259. 


FIG.  260. 


FIG.  261. 


the  universal  in  being  adjustable  only  to  height.  It  is  much 
less  expensive,  and  answers  equally  well  in  supporting  lenses, 
cardboard  screens,  jet-tubes,  etc.  Fig.  264  exhibits  a  good  form 
of  Test-Tube  Back,  and  Fig.  265  a  Test -Tube  Holder,  the  latter 


346 


PRACTICAL    PHYSICS. 


to  be  used  when  heating  a  solution  in  a  flame. 
small  heated  vessels,  or 
heated  substances,  the  Cru- 
cible Tongs  (Fig.  266)  will 
be  found  convenient.  The 
adjustable  Table  Support, 
(Fig.  267)  will  be  found 
useful  in  supporting  beak- 
ers, prisms,  etc.,  but  is  not 
indispensable.  Fig.  268  rep- 
resents the  Tinner's  Ni2-)- 
useful  instrument 


In  handling 


K) 


FIG.  262. 


pers,    a 


FIG. 


form. 


FlG.  264. 


FIG.  265. 


for  cutting  metals  in  sheet 

Fig.  269  is  a  Clamp  for  closing  -rubber  tubes.     Fig.  270 
shows  a    Cork  Borer   and   the  manner  of 
using  it.     A  small  round  file  makes  a  good 
substitute.      In 
reducing  the  size 
of   a   cork,  use 
a  flat  coarse-cut 
file.    To  prevent 

small  corks  splitting  when  drilling  holes  through  them,  wrap 
them  firmly  with  several  turns  of  stout  twine. 
In  perforating  rubber  corks,  keep  the  borer  wet 
with  a  solution  of  caustic  potash. 

In  electrical  work  a  few  good  battery  cells 
are  needed.  These  should  be  selected  in  view 
of  the  kind  of  service  required  of  them.  For 

intensity,    where 
constancy  is  imma- 
K3)  terial,  there  is  noth- 
266.  ing  better  than  the          FlG.  267. 


THE    PHYSICAL    LABOEATOEY. 


347 


Ghrenet  Battery    (Fig.  271),   charged    with    the    chromic   acid 

solution.  For  con- 
stancy, where 
strength  of  current 
is  not  so  much  of  an 
object,  the  Darnell's  FIG.  259. 

Batter  y  (Fig.  272)  is  superior  to  most  others.     The  forms  of 


FIG.  270. 

batteries  are  legion,  but  for  cheapness  and  efficiency  there  is 
none  superior  to 
the  two  men- 
tioned. It  is  too 
expensive  to  rely 
upon  batteries 
for  such  currents 
as  are  required 
for  electric  light- 
ing. Here  resort 
must  be  had  to 
the  Dynamo. 
Small  ones  are 
now  to  be  had 
giving  one  small 
arc  light,  suit- 
FIG.  27i.  able  for  optical  FlG.  273. 


348  PRACTICAL    PHYSICS. 

work,  for  about  $100.  Mr.  Geo.  M.  Hopkins,  in  the  Supplement 
to  the  "  Scientific  American,"  No.  600,  gives  full  directions 
for  constructing  such  a  dynamo.  Where  water  or  steam  power 
is  available,  there  is  no  more  important  instrument  for  the 
physical  laboratory  than  the  dynamo,  on  account  of  the  strong 
light  that  can  be  obtained  from  it.  Sunlight  is  so  uncertain, 
that  if  optical  work  is  made  dependent  on  such  a  source  of 
light  many  a  disappointment  will  be  met  with,  and  considerable 
disorganization  of  the  work  will  result  therefrom. 

596.  Conducting  the  Work.  —  Probably  the  greatest 
drawback  to  carrying  on  experimental  work  in  physics  is  the 
apparent  impossibility  of  accommodating  such  large  numbers  of 
students  as  are  always  found  desirous  of  studying  the  subject. 
When  the  class  is  very  large  it  is  recommended  that  it  be 
divided  into  five  divisions,  one  division  to  meet  for  work  each 
day  for,  say,  two  hours,  working  in  sections  of  two  pupils  each. 
The  problems  should  be  assigned  a  few  days  in  advance,  that 
they  may  be  carefully  studied  in  all  their  parts  by  the  pupils 
before  entering  the  work-room,  so  that  no  time  will  be  lost  in  as- 
certaining what  is  to  be  done,  and  in  what  manner.  It  is  also 
recommended  that  they  be  reviewed  by  the  instructor,  before  the 
class,  before  the  pupils  are  set  to  work  upon  them.  Each  pupil 
should  have  his  appointed  place  in  the  room,  where  his  work 
should  all  be  done,  except  where  the  nature  of  it  requires  a 
change.  The  apparatus  needed  for  his  work  should  be  placed  on 
his  table  in  advance,  say,  the  Saturday  before,  remaining  there 
during  the  week  for  the  use  of  the  different  sections.  When 
duplicate  pieces  of  apparatus  are  not  on  hand,  and  several  pupils 
require  the  same  piece  at  some  stage  of  their  work,  a  special  table 
had  better  be  provided  for  such  appliances  where  they  may  be 
found  when  needed.  This  is  more  especially  true  of  the  air- 


THE    PHYSICAL    LABORATORY.  349 

pump,  whirling-machine,  Atwood's  machine,  electrical  machine, 
etc.  On  completing  an  experiment  the  pupil  should  be  required 
to  make  carefully  worded  notes  on  all  that  he  has  observed.  This 
record  should  be  submitted  for  approval  immediately  after 
completing  the  experiment,  and  if  found  correct,  as  well  as 
complete,  in  all  its  parts,  then  the  next  experiment  can  be 
entered  upon  ;  but  if  unsatisfactory,  the  pupil  should  return  to 
the  same  experiment,  and  repeat  it  till  all  errors  are  corrected 
and  omissions  supplied  as  far  as  possible. 

When  the  classes  are  small,  or  assistance  is  furnished  the 
instructor,  the  number  of  hours  devoted  to  experimental  work 
should  be  increased.  Four  or  six  hours  per  week  spent  in  the 
laboratory,  and  perhaps  three  in  the  recitation-room,  drilling  on 
principles  and  reviewing  the  facts  developed  by  experiment, 
when  carried  on  for  a  school  year,  will  demonstrate  that  there  is 
no  study  in  the  curriculum  that  surpasses  physics  in  the  breadth 
of  mental  discipline  imparted. 

It  is  not  expected  that  each  pupil  will  attempt  all  the  work 
described  in  this  book,  but  a  judicious  selection  should  be  made, 
giving  each  pupil  some  work  under  each  topic,  the  amount  to 
be  determined  by  the  time  available,  the  aptness  of  the  pupil, 
and  the  laboratory  facilities.  Many  topics  might  be  omitted 
entirely,  and  if  found  desirable  the  order  of  the  others  might  be 
changed,  if  by  so  doing  there  is  secured  a  closer  conformity  to 
the  order  found  in  the  text-book  used  in  the  class-room. 

The  following  list  of  articles  selected  from  the  preceding 
pages  is  suggested,  as  offering  a  fairly  complete  and  eas}r 
course,  supplementing  to  good  purpose  the  experiments  of  the 
recitation-room  :  — 

2,  4,  5,  9,  12,  13,  18,  20,  24,  25,  31,  C2,  64,  67  to  70, 
73,  78,  79,  83,  84,  108  to  123,  137  to  148,  151  to  163,  182  to 
197, 216,219,222,  234,  239,  241,  246,  247,  253,254,  269  to  274, 


350  PRACTICAL    PHYSICS. 

285  to  300,  306  to  312,  315  to  322,  325,  326,  331,  346  to  353, 
358  to  361,  378  to  382,  386,  387,  391,  412  to  416,  428,  429, 
431,  434,  441  to  443,  452,  454,  456,  472,  476,  483,  485, 
491,  492,  504,  511,  512,  516,  517,  521,  522,  528,  530,  532,  534, 
539,  541,  545,  547,  548,  558,  561,  564. 

In  response  to  numerous  inquiries  from  teachers,  concerning 
physical  apparatus,  and  where  it  can  be  bought  at  fair  prices, 
the  author  would  take  this  occasion  to  say  that  anything 
described  in  the  preceding  pages  can  be  furnished  by  either 
Eberbach  and  Son,  Ann  Arbor,  Mich.  ;  E.  S.  Ritchie  and  Sons, 
Brookline,  Mass.  ;  A.  P.  Gage,  Boston,  Mass.  ;  or  Jas.  W. 
Queen  &  Co.,  Philadelphia,  Pa.  By  writing  to  either  of  these 
houses,  and  referring  to  the  articles  and  figures  of  this  book, 
you  can  promptly  learn  at  what  prices  the  various  appliances 
can  be  obtained.  The  author  will  gladly  give  any  information 
in  his  power  regarding  apparatus,  answer  any  questions  as  to 
its  use,  and  aid  teachers  in  any  way  he  can  in  overcoming  diffi- 
culties encountered  in  endeavoring  to  teach  physics  on  the  plan 
outlined  in  these  pages. 

597.  The  Note-Book.  —  Every  pupil  must  supply  him- 
self with  a  note-book  in  which  to  record  the  transactions  of  the 
laboratory.  This  book  should  be  a  model  of  neatness ;  work 
slovenly  done  should  be  rejected,  and  the  pupil  should  be  re- 
quired to  rewrite  it.  The  use  of  loose  sheets  of  paper  for  note- 
taking  should  not  be  permitted.  Calculations  and  sketches 
should  be  shown  on  the  left-hand  page,  and  observations,  descrip- 
tions, formulae,  and  theory  on  the  right-hand  page.  During  the 
evening  following  the  day  devoted  to  experimentation,  the  pupil 
should  prepare  a  full  report  of  his  day's  work,  describing  the 
character  of  each  experiment,  the  nature  of  the  apparatus  em- 
ployed, the  results  obtained,  and  the  inferences  which  he  thinks 


THE    PHYSICAL    LABORATORY.  351 

can  be  deduced  from  them.  After  these  reports  have  been 
examined  by  the  instructor,  and  the  errors  which  were  pointed 
out  corrected  by  the  pupil,  they  should  be  neatly  copied  into 
a  second  book  provided  for  the  purpose.  One  recitation-hour 
per  week  may  be  very  profitably  devoted  to  the  consideration 
of  these  reports  in  the  presence  of  the  whole  class,  the  in- 
structor passing  upon  their  accuracy,  completeness,  and  literary 
execution. 

598.  The  Graphic  Method.  —  This  method  is  frequently 
employed  to  find  out  the  probable  form  of  the  law  connecting 
two  quantities  which  are  so  related  that  a  change  in  one  is 
attended  by  a  change  in  the  other ;  as,  for  instance,  in  Art.  74, 
where  an  increase  in  the  weight  placed  in  the  pan  produces 
a  change  in  the  length  of  the  wire,  and  in  Art.  88,  where  a 
change  in  the  temperature  of  the  solvent  is  attended  by  a 
change  in  the  solubility  of  the  substance.  It  consists  in  repre- 
senting by  a  line  the  data  obtained  by  the  observer  in  the  course 
of  his  investigations,  the  shape  of  the  line  indicating  the  form 
of  the  law  connecting  the  dependent  facts.  To  construct 
the  line,  procure  a  piece  of  cross-section  paper  of  suitable  size. 
This  is  merely  a  good  quality  of  writing-paper  divided  into 
equal  small  squares,  by  a  great  number  of  horizontal  and  verti- 
cal lines,  the  most  desirable  sizes  for  these  squares  being  1  mm. 
or  .1  inch  on  a  side.  Such  paper  can  be  purchased  of  any 
dealer  in  mathematical  instruments.  Now  select  some  suitable 
scale  to  be  used  in  representing  the  things  to  be  compared,  the 
chief  condition  being  that  the  units  be  such  as  to  bring  all  the 
work  on  one  sheet.  For  instance,  in  Art.  74,  the  number  of 
units  of  weight  used  each  time  may  be  represented  by  as  many 
divisions  laid  off  on  one  of  the  horizontal  lines,  the  side  of  a 
square  serving  as  the  linear  unit.  If  this  is  found  to  require 


352  PRACTICAL    PlIYSIVti. 

too  long  a  line,  the  side  of  a  square  may  represent  two  or  more 
units  of  weight ;  and,  on  the  other  hand,  if  the  line  is  too  short, 
a  larger  unit  may  be  chosen.  In  like  manner  any  convenient 
unit  may  be  selected  to  represent  the  elongation  of  the  wire. 
After  suitable  units  have  been  decided  on,  not  necessarily  the 
same  for  both  quantities,  then  measure  toward  the  right  on 
the  horizontal  line,  passing  through  the  corner  of  some  one  of 
the  squares  (usually  taken  near  the  lower  left-hand  corner  of  the 
sheet,  and  called  the  origin}  a  sufficient  number  of  spaces  and 
parts  of  a  space  to  represent  the  numerical  value  of  the  first  of 
the  dependent  quantities,  and  then,  in  the  perpendicular  through 
the  point  just  located,  measure  off  a  distance  to  represent  the 
numerical  value  of  the  second  quantity,  marking  with  a  cross 
the  point  thus  located.  In  like  manner,  locate  points,  using 
the  remaining  data,  making  all  measurements  from  the  same 
origin,  and  employing  the  same  units.  Negative  data  should 
be  measured  off  in  directions  exactly  opposite  to  those  used  for 
positive  quantities.  Through  the  points  located,  sketch  as 
smooth  and  symmetrical  a  curve  as  possible.  The  greater  the 
number  of  points,  and  the  closer  they  are  together,  the  better  it 
will  be  for  sketching  the  curve.  The  simpler  the  line  passing 
through  these  points,  the  less  complex  the  law  connecting  the 
quantities  ;  as,  for  instance,  a  straight  line  would  imply  that  one 
quantity  is  proportional  to  the  other.  On  account  of  the  errors 
which  unavoidably  enter  into  all  observations,  the  points  will 
not  all  lie  exactly  on  a  smooth  curve,  but  may  be  a  little  to  one 
side  of  it.  Thus,  the  Graphic  Method  often  portrays  to  the  eye 
just  where  mistakes  have  been  made  by  the  observer,  and  also 
enables  him  to  get  approximate  values  for  intermediate  points 
in  the  problem.  See  Stewart  and  Gee's  Practical  Physics, 
Vol.  I.,  page  275. 


THE    PHYSICAL    LABORATORY.  353 

599.    Summary    of    Laboratory    Rules.  —  Pupils    are 
advised  to  observe  carefully  the  following  :  — 

1.  Be  orderly  and  neat  in  manipulation.     Keep  all  apparatus 
clean,  never  setting  away  any  apparatus  without  wiping  it  with 
a  chamois,  if  metal,  and    if  glass,  washing  it  and  thoroughly 
drying  it. 

2.  Economize  time  by  remembering  that  frequently  two  or 
more  operations  can  be  carried  on  simultaneously  ;  never,  how- 
ever, if  either  one  needs  close   and  constant  attention  during 
any  considerable  period  of  time. 

3.  Prepare  thoroughly  for  every  experiment,  so  that  every 
condition  will  be  observed,  and  no  failures  result  from  a  neglect 
of  some  requisite.     Do  not  substitute  for  what  is  the  best  pos- 
sible, that  which  will  barely  do. 

4.  Ascertain  the  reason   for  every  step  taken  in  working 
through   an   experiment,   noting  which  are  essential  conditions 
permitting  no  variations,   and  which  are  non-essential   only  in 
so  far  as  they  conduce  to  greater  accuracy,  and  hence  may  be 
modified  as  lack  of  apparatus  may  compel. 

5.  Be   exact  and  methodical.     Let  nothing  pass  unnoticed, 
although  you  may  not  see  its  significance  at  the  moment. 

6.  Keep  your   note-book  by  you,  and  record  in  it  carefully, 
neatly,  and  at  the  time  the  results  of  the  observations,  and  also 
make  sketches  of  the  apparatus  used. 

7.  Do  not  crowd  the  notes;  leave  plenty  of  room  after  each 
experiment  to  write  out  a  full  explanation  of  the  facts,  together 
with  the  principles  revealed  by  them.     If  several  similar  quan- 
tities are  recorded,  arrange  them  in  tabular  form  with  parallel 
columns. 


354  PRACTICAL    PHYSICS. 


APPENDIX   B. 
LABORATORY      OPERATIONS. 

600.  Cutting  Glass.  —  To  cut  small  glass  tubes,  make  a 
deep  scratch  with  a  three-cornered  file  across  the  tube  as  it  rests 
on  the  table  ;  then  holding  the  tube,  as  shown  in  Fig.  273,  with 

the  scratch  turned  from 
you,  press  suddenly  out- 
ward with  the  thumbs, 
and  it  will  break  off  as 
desired.  To  cut  off  large 
tubes,  flasks,  bottles, 
etc.,  make  a  deep  scratch 

.b  IG.  27o* 

with  a  file,  then  apply  to 

it  either  a  pointed  piece  of  glowing  charcoal,  a  heated  metal 
rocjj  or  a  fine  gas-jet.  The  sudden  expansion  by  heat  will 
generally  produce  a  crack ;  if  not,  then  touch  the  heated  spot 
with  a  wet  stick.  A  crack  thus  started  may  be  led  in  any 
desired  direction  by  keeping  the  source  of  heat  moving  slowty 
a  few  millimetres  in  front  of  it  as  it  advances.  To  get  a 
small-pointed  gas-flame  for  the  above  purpose,  connect  a  glass 
jet-tube  to  the  gas-supply  by  a  piece  of  rubber  tubing. 
Another  way  to  cut  a  glass  cylinder  is  to  wind  a  turn  of  fine 
platinum  wire  around  it,  just  where  the  scratch  has  been  made, 
bringing  the  ends  as  close  together  as  possible  without  touch- 
ing. Now  pass  through  the  wire  an  electric  current  of  suffi- 


LABORATORY    OPERATIONS. 


355 


cient  intensity  to  bring  the  wire  to  a  white  heat.  Glass  plates 
are  readily  cut  with  the  common  "  glass-cutter,"  an  instrument 
provided  with  a  highly-hardened  steel  wheel  in  place  of  a  point. 

601.  Smoothing  the  End  of  a  Glass  Tube. —  Warm 
the  end  by  passing  it  to  and  fro  through  the  Bunsen,  or  spirit 
flame  ;  then  hold  it  obliquely  in  the  flame,  with  the  end  just  in- 
serted,  slowly  turning   the   tube    around.     Remove    from   the 
flame  soon   after  the  flame  becomes  a  bright  yellow.     In  the 
case  of  large  tubes  it  will  be  necessary  to   smooth   them  by 
grinding  on  a  smooth  flag-stone  wet  with  water. 

602.  Bending  Tubes.  —  Warm  the  tube  for  several  inches 
each   side    of    the    place 

where   the  bend  is  to  be 

by    slowly    passing   it 

through  the  flame ;    then 

bring    the   tube   into    the 

gas-flame,  slowly  rotating 

it  on  its  axis,  heating  it 

evenly    for    about    three 

centimetres.      When    the 

flame  becomes  a  bright 
yellow  the 
tube  will  be 
soft.  Then 

gently  bend  the  ends  from  you  until  the  required 
angle  is  obtained.  Fig.  274  shows  how  to  hold 
the  tube.  In  bending  moderately  large  tubes  a 
flat  flame  is  preferable.  Fig.  275  exhibits  an 
attachment  for  the  Bunsen  burner  to  produce 
FIG.  275.  such  a  flame.  The  fish-tail  gas-burner  or  the 


FIG.  274. 


356  PRACTICAL    P//rN/Y'S'. 

kerosene  lamp  gives    a   very  suitable  flame  for  use  in  bending 
small  tubes. 

603.  Closing  the  End  of  a  Tube.  —  Soften  the  tube 
at  the  end  by  holding  it  in  the  flame,  and  then  pull   the  end 
out  with  another  piece  of  glass.     Keep  removing  the  small  tail 
that  is  left  till  it  becomes  quite  small ;   then  heat  the  end  for  ji 
few  minutes,  turning  the  tube   in   the  fingers.     If  the   tube  is 
held  in  an  inclined  position  in  the  flame,  the  opening  will  keep 
contracting  till  finally  it  closes  up. 

604.  Drawing  out  Tubes.  —  Thoroughly  soften  the  tube 
uniformly  for  three    centimetres    of    its    length,   then    remove 
from   the   flame    and  pull  the   parts  asunder  till  the  diameter 
is  about  1  mm.,  holding  the  tube  steadily  till  it  cools,  to  avoid 
crooking  it.     Now  scratch  it  wTith  a  file  at  the  smallest  part  and 
break  it  in  two,  smoothing  the  ends  in  the  flame. 

605.  Drilling  Holes  in  G-lass.  —  Small  holes  are  quite 
readily  drilled  through  glass  by  using  a  hard  drill,  wet  with  a 
solution  of   camphor  in   oil  of   turpentine.     A  three-cornered 
file,  with  the  end  broken  oft%,  makes   a  good  drill  for  glass. 
Large  holes  may  be  drilled  with  a  brass  tube  and  emery  powder 
moistened  with  water.     A  piece  of  wood,  with  a  hole  in  it  of 
the  required  size,  cemented  to  the  glass  plate,  makes  an  excel- 
lent guide  for  the  drill.     The  tube  can  be  rotated  by  the  fingers, 
or  if  a  wooden  pulley  is  attached  to  it,  the  common  drill-stock 
bow  may  be  used.     If  the   drill   is  moistened  with  a  paste  of 
fluor-spar  and  sulphuric  acid,  the  labor  of  drilling  glass  is  much 
lessened. 

606.  Drawing    on    G-lass.  —  Drawings  in  India-ink   for 
lantern  projections  are  easily  executed  on  glass  by  first  flowing 


LABORATORY    OPERATIONS.  357 

the  plate  with  a  solution  of  plain  collodion,  and  allowing  it  to 
dry.  As  the  transparency  is  not  in  the  least  affected,  the  plate 
may  be  placed  directly  over  the  picture  to  be  reproduced,  and 
traced  in  India-ink  with  a  fine  steel  pen,  even  by  one  having 
little  or  no  artistic  skill. 

607.  Useful  Cements.  —  Frequent  use  will  be  found  for 
reliable     cements.       The     following    are    confidently    recom- 
mended :  — 

For  cementing  wood,  leather,  metal,  or  glass  to  glass,  melt 
at  100°  C.  one  part  of  gutta-percha  and  one  part  of  pine-pitch, 
stirring  till  homogeneous.  Soften  the  cement  by  heat  when 
needed  for  use. 

For  an  acid-proof  cement,  make  a  concentrated  solution  of 
sodium  silicate,  and  form  a  paste,  with  powdered  glass. 

For  work  in  electricity  an  excellent  insulating  cement  is  made 
by  melting  together  rosin,  3J  Ibs.,  beeswax,  2J  Ibs.,  Venetian- 
red,  2  Ibs.,  and  Venice  turpentine,  12  oz.  Less  Venice  tur- 
pentine will  make  it  harder. 

608.  Silvering  Glass.  —  Dissolve    154   grains   of    silver 
nitrate  in   17  fluid  ounces  of  distilled  water.     Add  ammonia 
water  until  the  precipitate  formed  is  nearly  redissolved.     Filter 
and  add  distilled  water,  so  as  to  make  the  whole  34  fluid  ounces. 
This  gives  solution  A.     Thirty-one  grains  of  silver  nitrate  are 
dissolved  in  34  fluid  ounces  of  boiling  distilled  water  ;  dissolve 
23  grains  of  Rochelle  salt  in  a  small  quantity  of  water,  add  it 
to  the  boiling  nitrate,  boil  till  the  precipitate    becomes   gray. 
Filter  and  allow   to  cool.     This  gives  solution  B.     Clean  the 
glass  object  perfectly  by  rubbing  it  with  strong  nitric  acid, 
using  a  stick  for  the  purpose.     Wash  off  the  acid,  then  wash 
the  article  with  caustic  potash,  then  with  alcohol,  and  finally 


358  PRACTICAL    PJrrSTC8. 

with  distilled  water.  Place  the  object,  with  the  side  uppermost 
which  has  to  be  silvered,  in  a  clean  dish,  and  while  still  wet 
pour  over  it,  and  mix  equal  quantities  of  the  solutions  A  and  B, 
covering  it  half  an  inch.  In  about  two  hours,  according  to  the 
temperature,  the  silvering  is  complete  ;  the  hotter  the  quicker  ; 
the  slower  the  better.  The  object  is  now  taken  out,  cleaned  of 
its  superfluous  silver,  dried,  and  varnished.  If  the  coating 
is  thick,  the  silver  surface  may  be  polished  with  rouge  powder 
on  cotton-wool. 

609.  Cleaning  Mercury.  —  Mercury  is  an  absolute  neces- 
sity in  many  lines  of  investigation.     During  its  use  it  is  liable 
to  become  alloyed  with  zinc  or  tin,  or  both,  rendering  it  unfit  for 
the  service  required  of  it  in  experimenting.     To  remove  these 
metals  proceed  as  follows :  To  every  100  parts  of  mercury  add 
10  parts  of  a  strong  solution  of  ferric  chloride  and  100  parts  of 
water.     Shake  in  a  strong  bottle  till  thoroughly  mixed,  the  mer- 
cury becoming  broken  up  into  small  globules.    Set  aside  for  two 
or  three  days  in  a  cool  place,  then  decant  off  the  liquid  from 
the  mercury,  and  afterwards  wash  thoroughly  by  shaking  it  up 
again  with  dilute  hydrochloric  acid,  and  finally  with  hot  water. 
Remove  with  porous  paper  as  much  of  the  water  as  possible  ; 
.then  pour  into  a  filter  having  a  small  pin-hole  in  the  bottom, 
and  finally  dry  over  a  water-bath. 

610.  Soldering. — Prepare    a   soldering   fluid   by   adding 
scraps  of  zinc  to  hydrochloric  acid  till  it  refuses  to  dissolve  any 
more.     Wet  the  surfaces  to   be  joined  with  this  fluid,   place 
between  them  a  few  pieces  of  soft  solder,  an  alloy  of  lead  and 
tin ;  then  apply  heat  either  by  holding  the  article  in  a  flame,  by 
touching  it  with  a  heated  soldering-iron  till  the  solder  melts,  or 
by  directing  upon  it  a  blow-pipe  flame  ;  on  cooling,  the  surfaces 
will  be  firmly  joined  together. 


LABOEATOEY    OPERATIONS.  359 

611.  Amalgamating  Battery-Zincs.  —  Dissolve  15  com. 
of  mercury  iii  a  mixture  of  170  ccm.  of  nitric  acid  and  625 
ccm.   of  hydrochloric  acid.     Keep  the  liquid  in   a  glass-stop- 
pered bottle.     To  use,  immerse  the  zinc  in  the  fluid  for  a  few 
aiinutes,  then  remove,  and  rinse  thoroughly  in  water. 

612.  Battery    Fluids    for    the    Carbon    and    Zinc 
Battery. 

No.  1.  — Water,  8  kilo.  ;  pulverized  potassium  bichromate,  1.2 
kilo.  ;  sulphuric  acid,  3.6  kilo.  Put  the  powdered  potassium 
bichromate  in  the  water,  and  when  dissolved  add  the  acid  in  a 
fine  stream,  with  constant  agitation. 

No.  2. — Dissolve  4  oz.  of  chromic  acid  in  one  quart  of 
dilute  sulphuric  acid,  1  vol.  sulphuric  acid  to  12  of  water,  and 
allow  the  solution  to  cool  and  settle. 

The  last  of  these  solutions  is  greatly  to  be  preferred  to  the 
former,  as  the  absence  of  potassium  prevents  the  formation  of 
chrome  alum  crystals,  the  defect  of  the  first  solution.  Chromic 
acid  can  now  be  obtained  at  greatly  reduced  prices,  and  pro- 
duces a  solution  lasting  much  longer  than  that  prepared  from 
the  bichromate. 

As  the  chromic  acid  solution  is  frequently  used  as  a  de- 
polarizer in  the  Bunseu  battery,  the  following  preparation  from 
chromic  acid  will  be  found  very  efficient :  Dissolve  one  pound  of 
chromic  acid  in  one  part  of  water,  and  add  seven  fluid  ounces 
of  sulphuric  acid,  with  stirring.  It  is  claimed  that  the  con- 
stancy is  improved  by  adding  one- third  volume  of  nitric  acid. 

613.  Care  of  Batteries.  —  All  the  connections  in  a  bat- 
tery must  be  kept  clean  and  bright,  and  the  zincs  well  amalga- 
mated.    The  porous  cups  must  be  thoroughly  soaked  in  water 
before  using,  and  kept  in  water  while  the  battery  is  idle.     In 


360  PRACTICAL    PHYSICS. 

the  Daniell's  battery  they  become  clogged  in  time  with  copper, 
and  hence  useless.  They  can  be  renovated  by  soaking  in  nitric 
acid,  but  it  is  probably  just  as  cheap  to  throw  them  away  and 
substitute  new  ones.  In  the  carbon  battery,  where  the  potas- 
sium bichromate  solution  is  used,  the  carbons  become  clogged 
with  chrome  alum  crystals  and  chromium  oxide,  greatly  increas- 
ing the  resistance.  If  the  carbons  are  soaked  for  an  hour  in 
nitric  acid  the  difficulty  will  be  removed.  Chromium  oxide  is 
formed  in  the  case  of  the  chromic  acid  solution,  and  in  time 
affects  the  action  of  the  battery. 

It  often  happens  that  the  carbons  become  detached  from  the 
brass  clamp  in  the  case  of  the  Grenet  battery,  and  need  to  be 
resoldered,  a  thing  easily  done  if  the  end  of  the  carbon  is  first 
plated  with  copper.  To  do  this,  connect  to  the  negative  pole 
of  a  Daniell's  battery  the  carbon  plate,  and  to  the  other  a 
strip  of  copper.  Let  these  dip  close  together,  but  not  in 
contact,  in  a  vessel  containing  a  solution  of  copper  sulphate, 
removing  them  when  the  plating  covers  completely  the  surface 
to  be  soldered.  Cover  with  beeswax  the  surface  not  to  be 
plated. 

614.  Electrical  Amalgam.  —  Take  two  parts  by  weight 
of  tin,  one  part  of  zinc,  and  eight  parts  of  mercury.     Melt  the 
tin  in  an  iron  ladle,  add  the  zinc,  and  raise  it  to  the  melting- 
point.     Now  add  the  mercury,  and  stir  the  mixture  till  it  is 
cool.     Apply  to  the  rubber  by  mixing  with  the  amalgam  a  little 
lard. 

615.  Cleaning  Electrical  Machines.  —  To  remove  dust 
from  electrical  machines,  use  a  cloth  wet  with  kerosene  oil. 
The  efficiency  of  both  the  Frictional  and  the  Holtz  Machine  is 
frequently  largely  increased  when  this  is  done.     Even  the  old 
form  of  Holtz  machine  seldom  fails  to  work  when  treated  in 
this  way. 


TABLES    FOE    REFERENCE. 


361 


APPENDIX    C. 


TABLES      FOR      REFERENCE. 

Table    I. 
CAPILLARITY. 

Height  to  which   the   liquid  will    rise   in   a   tube  1  mm.  in 
diameter :  — 
Alcohol    .  .11.4  mm.    '    Mercury — 9.2  mm. 


Bromine 9.0 

Ether  .  9.5 


Turpentine 12.7 

Water  .  29.3 


Table    II. 


DENSITIES    OF    VARIOUS    SUBSTANCES. 


Benzine 0.72  to  0.740 

Benzole 0.899 

Birch 0.690 

Bismuth,  cast 9.822 

Blood 1.0(50 

Boxwood 1.280 

Brass,  cast 8.400 

Brass,  sheet 8.440 

Brick  ......     1.6  to  2.000 

Bromine 3.187 

Butter ,     .     .     0.942 

Calcium  chloride    ....     2.230 

Camphor 0.988 

Carbon  disulphide  .  .  .  .  1.293 
Carbon  dioxide,  liquid  .  .  0.947 
Cedar,  American  ....  0.554 
Chalk  .  1.8  to  2.800 


Acetic  acid    .     .     . 

.     .     .     1.060 

Agate  

.     .     .     2.615 

Alcohol,  absolute  . 

.     .     .     0.806 

Alcohol,  common  . 

.     .     .     0.833 

Alum  

.     .     .     1.724 

Aluminium    . 

.     .     .     2.670 

Amber      .... 

.     .     .     1.078 

Antimony,  cast. 

.     .     .     6.720 

Apple-tree  wood     . 

.     .     .     0.790 

Arsenic    .... 

.     .     .     8.310   ' 

Ash,  dry  .... 

.     .     .     0.690 

Ash,  green    .     .     . 

.     .     .     0.760 

Asphalt    ...... 

.     .     .     2.500 

Basalt       .          .     . 

.     .     .     2.950   ! 

Beech,  dry    .     .     . 

0.690  to  0.800   | 

Beeswax       .     .     . 

.     .     .     0.964 

Bell-metal    .     .     , 

.     .     .     8.050 

362 


PRACTICAL    PHYSICS. 


Cherry-tree  .     .     «     .     .     .  0.710 

Chestnut 0.606 

Chloroform 1.525 

Clay 1.920 

Coal,  anthracite      .     .  1.26  to  1.800 

Coal,  bituminous    .     1.270  to  1.423 

Cobalt 8.800 

Concrete,  ordinary      .     .     .  1.900 

Concrete,  in  cement   .     .     .  2.200 

Cork 0.240 

Copper,  cast 8.830 

Copper,  sheet 8.878 

Deal,  Norway 0.689 

Diamond 3.530 

Earth 1.520  to  2.000 

Ebony 1.187 

Elder 0.690 

Elm     ........  0.579 

Elm,  Canadian       .     .     .     .  0.725 

Emery 3.900 

Ether 0.736 

Emerald 2.770 

Feldspar 2.600 

Fir,  spruce 0.512 

Fluor-spar 3.200 

Galena e  7.580 

German-silver 8.432 

Glass,  flint    .     .     .     3.000  to  3.600 

Glass,  crown 2.520 

Glass,  plate 2.760 

Glycerine 1.260 

Gold 19.360 

Gypsum,  crys.  .     ,     .     .     .  2.310 

Granite 2.650 

Graphite 2.500 

Gun-metal 8.561 

Gutta-percha 0.966 

Heavy  spar 4.430 

Honey 1.450 

Human  body 0.890 

Hydrochloric  acid,  aq.  sol.  .  1.222 


Ice 0.917 

Iceland  spar 2.723 

Iron,  bar  .......  7.788 

Iron,  cast 7.230 

Iron,  wrought 7.780 

India-rubber      ....  0.930 

Iodine       .....     =     .  4.950 

Iron  pyrites  .     .     .     .     .  5.000 

Ivory ,     .     .  1.820 

Lard    ....,.,.  0.947 

Lead,  cast     ......  11.360 

Lead,  sheet  ......  11.400 

Lignum  vitae     .     .     .     .     ,  1.333 

Lime,  quick 0.843 

Limestone      ......  3.180 

Logwood 0.913 

Magnesium 1.750 

Mahogany    .     .     .     .  0.56  to  0.852 

Maple 0.755 

Marble 2.720 

Mercury ,     .  13.596 

Milk 1.032 

Molasses  .......  1.426 

Mortar,  average     ....  1.700 

Naphtha 0.848 

Nitric  acid    .     .     .     .  1.38  to  1.559 

Oak,  American  red     .     .     .  0.850 

Oak,  American  white       .     .  0.779 

Oak,  live,  seasoned     .     .     .  1.068 

Oak,  live,  green     .     .     .     .  1.260 

Oil,  castor    .     .     .     .     „     .  0.970 

Oil,  linseed  ......  0.940 

Oil,  olive 0.915 

Oil,  turpentine 0.870 

Oil,  whale     ......  0.923 

Paraffine  .     ,     .     .     0.824  to  0.940 

Petroleum 0.836 

Phosphorus 1.830 

Pear-tree 0.660 

Pine,  red,  dry 0.590 

Pine,  white,  dry     ....  0.554 


TABLES    FOE    REFERENCE. 


363 


Pine,  yellow,  dry  .     .     .     .  0.461 

Pine,  pitch 0.660 

Pitch 1.150 

Platinum  wire 21.531 

Poplar,  common    ....  0.389 

Porcelain,  china     .     .     .     .  2.380 

Potassium 0.865 

Quartz 2.650 

Rock-salt 2.257 

Saltpetre 2.100 

Sand,  quartz 2.750 

Sand,  river 1.880 

Sand,  fine 1.520 

Sand,  coarse 1.510 

Silver,  cast  .     .       10.424  to  10.511 

Slate 2.880 

Sodium 0.970 

The  above  table  gives  the  weight  in  grammes  of  1  ccm. 
of  the  substance.  It  should  be  considered  as  giving  only 
approximations,  as  most  of  the  densities  vary  between  wide 
limits  in  different  specimens. 

GASES    AIVD    VAPORS  AT   O°  C.,  BAROMETRIC    PRESSURE 

OF    76    CM. 


Steel,  uuhammered    .     .     .  7.816 

Sugar,  cane  ......  1.593 

Sulphur,  native      ....  2.033 

Sulphuric  acid  ...          .1.840 

Tallow      .......  0.940 

Tar      ....                    .  1.015 

Tin,  cast  .......  7.290 

Tourmaline,  green      .     .     .  3.150 

Vinegar .  1.026 

Water,  at  100°  C 0.958 

Walnut     ...          ...  0.680 

Water,  sea 1.027 

Wax,  white 0.970 

White  metal,  Babbitt      .     .  7.310 

Willow 0.585 

Zinc,  cast 7.000 


Acetic  acid  vapor      .     .     .  2.0800 

Air 1.0000 

Alcohol  vapor 1.6138 

Ammonia    ......  0.5967 

Benzole  vapor      ....  2.7290 

Carbonous  oxide  ....  0.9670 

Carbon  dioxide     ....  1.5241 

Chlorine 2.4501 

Coal-gas      .     .     .      0.340  to  0.6500 

Cyanogen 1.8060 

Ether  vapor 2.5630 

Hydrochloric  acid     .     .     .  1.2780 

In  the  above  table  the  unit  adopted  is  the  quantity  of  matter 
in  1  ccm.  of  air  under  the  standard  conditions. 


Hydrogen  disulphide 
Hydrogen  .  .  .  . 
Hydriodic  acid  .  . 
Marsh  ga"  .  .  °  . 
Mercury  vapor  „  . 
Nitrogen  .  .  .  . 
Nitrogen  binoxide  . 
Nitrogen  monoxide  . 

Oxygen  

Sulphurous  acid  . 
Water  vapor    .     .     . 


1.1912 
0.0693 
4.3737 
0.5540 
6.9207 
0.9714 
1.0392 
1.5241 
1.1057 
2.2113 
0.6225 


364 


PliA  CT1CAL    PHYSICS. 


Table    III. 
LIMIT    OP    ELASTICITY. 


Cast  steel,  drawn 

.     .     55.6 

Platinum,  drawn  .     . 

.      .   2(1.  0 

"       "      annealed 

.     .       5.0 

"          annealed 

.     .     14.5 

Copper   drawn 

12  0 

Steel,  drawn  .... 

42.5 

"        annealed     .     . 

.     .       3.0 

"      annealed  . 

.     .     15.0 

Iron,  drawn    .... 

.     .     32.5 

Silver,  drawn 

.     .   11.25 

"     annealed     .     .     . 

.     .       5.0 

"       anneale'l 

,     .     2.75 

Lead,  drawn  .... 

.     .     0.25 

Tin,  drawn     .     .     . 

.     0.45 

"      annealed   . 

.     .       0.2 

"      annealed      .     .     . 

.      .     0.20 

The  above  table  gives  the  weight  in  kilogrammes  necessary 
to  cause  permanent  elongation  in  wires  1  mm.  in  diameter  at 
the  ordinary  temperature. 


Table   IV. 
ELECTRICAL    CONDUCTIVITY. 


4  24 

Lead  pressed 

7  67 

Aluminium,  annealed 
Bismuth,  pressed    . 
Brass 

.  51.64 
.     1.15 
26  22 

Mercury,  liquid  .  .  . 
Nickel,  annealed  .  .  . 
Platinum,  annealed 

.     1.58 
.   12.07 
.    16.61 

Cadmium       
Copper,  annealed   .     . 
German  silver    .... 
Gold,  annealed  . 

.   22.37 
.  94.19 
.     7.14 
.  71.83 

Silver,  annealed 
Sodium     ...... 
Tin,  pressed       .     .     .     . 
Zinc,  pressed 

100.0 
.   72.43 
.   11.39 
.  26.73 

The  above  table  expresses  the  conductivity  of  the  substances 
relatively  to  silver  at  0°  C. 


TAULES    FOE    REFERENCE. 


365 


Table    V. 

APPROXIMATE    ELECTRO-MOTIVE    FORCE    OF 
PRIMARY    BATTERIES. 

DanielFs,  amalgamated  zinc,  H2SO4  -f-  4Aq. ,  Cu  SC-4,  con.  sol.   1.079  volts. 

"  "        -j-12  "  "        0.978  " 

"  "        -j-12  Aq.,  Cu  NOs,      "        1.000  " 

"         equi-dense  solutions  of  Zn  864,  and  Cu  SC>4  plates 

of  pure  Zn  and  Cu 1.104  " 

Bunsen,  amal.  zinc,  H2SC>4  -\-  12  Aq.,  and  HNO3,  carbon  .     .     1  964  " 

Grove,  "      -j-  ^Aq. ,  HNOs,  platinum  1.95G  " 

Leclanche,  zinc  in  saturated  solution  of  NH4  Cl        .     .     .     .     1.32  " 

Potassium  bichromate 2.00  " 


Table    VI, 

ELECTRICAL    RESISTANCE,  DIAMETER,    CROSS-SECTION, 
ETC.,    OF    PURE      COPPER    WIRE,     BIRMING- 
HAM   GAUGE,     TEMPERATURE    15°    C. 


DIAMETER. 

AREA  OF  CROSS-SEC. 

RESISTANCE. 

WEIGHT. 

No. 

Ins. 

Cms. 

Sq.  Iiis. 

Sq.  Cms. 

Ohms, 
per  Yd. 

Ohms, 
per  M. 

Lbs.  per 
Yd. 

Grrns. 
per  M  - 

0000 

.454 

1.1530 

.1620000 

1.0444000 

.000152 

.000167 

1.884000 

934.700 

000 

.425 

1.0790 

.1420000 

.9150000 

.000174 

.000190 

1.651000 

819.100 

00 

.380 

.9650 

.1130000 

.7320000 

.000217 

.000238 

1.320000 

654.800 

0 

.340 

.7620 

.0908000 

.5860000 

.000272 

.000297 

1.056000 

524.200 

1 

.300 

.7210           .0707000 

.4560000 

.000349 

.000382 

.822000 

408.100 

2 

.284 

.7210 

.0693000 

.4090000 

.000389 

.000425 

.737000 

365.800 

3 

.259 

.6580 

.0527000 

.3400000 

.000468 

.000512 

.613000 

304.200 

4 

.238 

.6050 

.0445000 

.2870000 

.000554 

.000606 

.518000 

256.900 

5 

.220 

.5590 

.0380000 

.2450000 

.000649 

.000709 

.442000 

219.500 

6 

.203 

.5160 

.0324000 

.2090000 

.000762 

.000833 

.377000 

186.900 

1 

.180 

.4570 

.0254000 

.1640000 

.000969 

.001060 

.296000 

146.900 

366 


PRACTICAL    PJ/YtilVS. 


No. 

DIAMETER. 

AREA  OP  CROSS-SEC. 

RESISTANCE. 

WEIGHT. 

Ins. 

Cms. 

Sq.Ins. 

Sq.  Cms. 

Ohms, 
per  Yd. 

Ohms. 
perM. 

Lbs.  per   Gnus. 
Yd.    per  M. 

8 

.165 

.4190 

.0214000 

.1380000 

.001150 

.001260 

.249000 

123.5000 

9 

.148 

.3760 

.0172000 

.1110000 

.001430 

.001570 

.200000 

99.3000 

10 

.134 

.0*00 

.0141000 

.0910000 

.001750 

.001910 

.164000 

81.4000 

11 

.120 

.9806 

.0113000 

.0730000 

.002180 

.002380 

.132000 

65.5000 

12 

.109 

.2770 

.0093300 

.0602000 

.002640 

.002890 

.109000 

53.9000 

13 

.095 

.2410 

.0070900 

.0457000 

,003480 

.003800 

.082500 

40.9000 

14 

.083 

.2110 

.0054100 

.0349000 

.004560 

.004980 

.063000 

31.2000 

15 

.072 

.1830 

.0040700 

.0263000 

.006060 

.006620 

.047400 

23.5000 

16 

.065 

.1650 

.0033100 

.0214000 

.007430 

.008130 

.038600 

19.2000 

17 

.058 

.1470 

.0026400 

.0170000 

.009330 

.010200 

.030700 

15.3000 

18 

.049 

.1240 

.0018900 

.0122000 

.013100 

.014300 

.022000 

10.9000 

19 

.042 

.1070 

.0013900 

.0089400 

.017800 

.019600 

.016100 

8.0000 

20 

.035 

.0889 

.0009620 

.0062100 

.025600 

.028000 

.011200 

5.5600 

21 

.032 

.0813 

.0008040 

.0051900 

.030700 

.033500 

.009360 

4.6400 

22 

.028 

.0711 

.0006160 

.0039700 

.040000 

.043810 

.007160 

3.5500 

23 

.025 

.0635 

.0004910 

.0031700 

.050200 

.054900 

.005710 

2.8300 

24 

.022 

.0559 

.0003800 

,0024500 

.064900 

.070900 

.004420 

2.1900 

25 

.020 

.0508 

.0003140 

.0020300 

.078600 

.085800 

.003670 

1.8200 

26 

.018 

.0457 

.0002540 

.0016400 

.096900 

.106000 

.002960 

1.4700 

27 

.016 

.0406 

.0002010 

.0013000 

.123000 

.134000 

.002340 

1.1600 

28 

.014 

.0356 

.0001540 

.0009930 

.160000 

.175000 

.001790 

0.8890 

29 

.013 

.0330 

.0001330 

.0008560 

.186000 

.203000 

.001540 

.7660 

30 

.012 

.0305 

.0001130 

.0007320 

.218000 

.288000 

.001320 

.6530 

31 

.010 

.0254 

.0000785 

.0005070 

.314000 

.343000 

.000915 

.4540 

32 

.009 

.0229 

.0000636 

.0004100 

.388000 

.424000 

.000746 

.3670 

33 

.008 

.0203 

.0000503 

.0003240 

.491000 

.536000 

.000585 

.2900 

34 

.007 

.0178 

.0000385 

.0002480 

.641000 

.701000 

.000442 

.2200 

35 

.005 

.0127 

.0000196 

.0001270 

1.260000 

1.370000 

.000229 

.1130 

36 

.004 

.0102 

.0000126 

.0000811 

1.960000 

2.150000 

.000146 

.0720 

TABLES    FOR    REFERENCE. 


367 


Table    VII. 
ACCELERATION    DUE     TO     GRAVITY. 

Berlin,        lat.  52°30'  .  981.25  cm.  Washington,  lat.  38°54'  .  980.06  cm. 

Greenwich,"   51°29'  .  981.17    "  Lat.  of  45° 980.61    " 

Paris,  "    48°50'  .  980.94    "  Equator 978.10    " 

New  York,  "    40°43f  .  980.19    "  Pole ,  983.11    " 


Table    rill. 

HEAT,    ABSORBING,    CONDUCTING,    RADIATING, 
REFLECTING    POWER. 


Substance. 

,0 

II 

<1 

Conduct- 
ing. 

i* 

"S3 

J» 

Substance. 

Absorb- 
ing. 

Conduct- 
ing. 

IB 

1* 

fT 

1.8 

Lead  white... 

100 

100 

33.1 

7 

100 

77.6 

7 

Palladium  .... 

63 

90 

10 

Paper  

98 

Gold  polished  .  . 

53.2 

3 

8  4 

17 

Indian  Ink  

85 

85 

13 

2.8 

Shellac  

72 

72 

Isinglass  
Lampblack  
Lead  polished  .  . 

91 

100 

8  5 

80  " 
100 
19 

0 
60 

Silver,  polished 
Steel  
Tin  

100 
12.0 
14  5 

3 
12 

90 
70 

"      tarnished  . 

45 

Zinc  

In  the  table  of  absorbing  powers  the  standard  adopted  is 
lampblack  and  the  source  of  heat  is  copper  at  100°  C.  In  con- 
ducting powers,  silver  is  the  standard.  In  radiating  power, 
lampblack  is  taken  as  the  standard.  The  initial  temperatures 


868 


PRACTICAL    PHYSICS. 


of  the  substances  compared  is  100°  C. 
polished  brass  is  taken  as  the  standard. 


In  reflecting  powers, 


Table    IX. 
BOILING  POINTS  OF    SUBSTANCES  AT  BAR.  PRES.  76  CM, 


Acetic  acid  .  . 
\cetone  •  • 

.     .     119.00°  C. 
56  28 

Petroleum   .     .     . 

40  to  70.0°  ( 
290  0 

.     -.       78.39 

Sulphur 

.     .     448  4 

Aldehyde  .  .  . 
Ammonia  .  .  . 
Amylic  alcohol  . 
4.niline  .  .  . 

.     .       20.78 
.     .  —39.00 
.     .     131.00 
183  70 

Sulphuric  acid 
Suphur  dioxide     . 
Turpentine       .     . 
Water   distilled 

.     .     338.0 
.     .     —8.0 
.     .     159.3 
100  0 

Benzine  .  .  . 
Benzole 

90  to  110.00 
80  44 

Water,    saturated 
NaCl    .     . 

with 
102  0 

Bromine    .     .     , 
Carbon  dioxide   . 
Carbon  disulphide 
Ether 

.     .       63.00 

.     .  —78.00 
.     .       48.00 
34  90 

Water,   saturated 
KNO3        .     .     . 
Water,     saturated 
Ko  CO3 

with 
.     .      116.0 
witli 
135  0 

Iodine  .... 

.     .     200  00 

Water,     saturated 

with 

Mercury 

350  00 

CaCl2  .... 

.     .     179.0 

Nitrous  oxide 

.     .  —  92.00 

Zinc  

.     .  1040.0 

Methylic  alcohol 

.     .       65.5 

Table   X. 

COEFFICIENTS    OF    EXPANSION    FOR    1< 
0°    AND    100°    C. 

.  LINEAR. 


BETWEEN 


Aluminium    ....  0.00002221 

Antimony      ....  0.00000980 

Bismuth   .....  0.00001330 

Brass    ......  0.00001875 

Bronze 0.00001844 

Copper 0.00001866 

Ebonite 0.00008420 

Glass    .     .     ,     .     .     .  0.00000861 

Gold 0.00001466 

Graphite 0.00000786 

Iron,  cast       ....  0.00001125 

"     wrought    .     .     .  0.00001220 


Lead 0.00002799 

Marble 0.00000786 

Paraffine 0.00027854 

Pine 0.00000496 

Platinum 0.00000886 

Sandstone,  red  .     .     .  0.00001174 

Silver 0.00001943 

Sulphur 0.00006413 

Steel,  tempered       .     .  0.00001322 

"      untempered       .  0.00001095 

Tin 0.00002730 

Zinc  0-00002976 


TABLES  FOR  REFERENCE. 


369 


Air,  cons,  vol.,  0°-100°    , 

"     cons,  pres.,  0°-100° 

Alcohol,  ethyl.  0°-50°      . 

"       methyl.  0°-61°  . 


CUBICAL. 

0.003663  Ether,  0°-63°  ....  0.002100 
0.003667  Mercury,  0°-100°  .  .  .  0.000181 
0.001080  Sulphuric  acid,  0°-30°  .  0.000489 
0.001358  Turpentine,  — 9°-106°  .  0.001050 


Benzine,  11°-81°    .     .     .  0.001385       Water,  4°-100°  ....  0.000449 


Table 


LATENT    HEAT  OF  LIQUEFACTION    AND  VAPORIZATION. 

LIQUEFACTION. 


Beeswax 97.22 

Bismuth 12.64 

Lead.     . 5.37 

Mercury      ......  2.83 

Phosphorus 5.03 

Platinum .27.18 

Potassium  nitrate      .     ,     .  47.37 


Silver 21.07 

Sodium  nitrate     ....  62.97 

Sulphur 9.37 

Tin 14.25 

Water 79.24 

Zinc  .  28.13 


VAPORIZATION. 


Alcohol,  ethylic      ....  202.4 

"         methylic  ....  264 

Acetic  acid    ......  102 

Bromine  .......  45.6 

Carbon  disulphide      ...  86.7 


Ether 90.4 

Mercury 62.0 

Oil  of  turpentine    ....  74.0 

Water.                                   ,  535.9 


Table    XII. 


MELTING    POINTS 


Antimony 425°   C. 

Beeswax 62° 

Bismuth 270° 

Brass 1020° 

Bromine —24.5° 

Butter 33.0° 

Copper    .     .     1064.0°  to  1200° 

German-silver     .     .     .  1093° 

Gold      ......  1250.0° 

Ice  .  0.0° 


Iridium      .     .     .     .     .     1950.0°  C. 
Iron      .     .      1500.0°  to  1600° 

Lard 33.2° 

Lead 334° 

Margaric  acid     .     .     .         59.9° 

Mercury —38.8° 

Paraffine   ....     38°-52° 
Phosphorus   ....         44.2° 
Platinum.     .     1775°  to  2000° 
Potassium  02.5° 


370 


PRACTICAL    PHYSICS. 


Rose's  metal  ....  94°  C. 

Silver 1000° 

Sulphur 115° 

Sodium 97.6° 

Stearic  acid    ....  69.9° 

Stearine 60° 

Spermaceti     ....  49° 


Tallow  (fresh)    ...         43°  O. 


Tin  .    .     .     . 

Turpentine  . 
Wax,  white  . 
Wood's  metal 
Zinc 


235° 

—27° 

65° 

68° 

433° 


Table    XIII. 
SPECIFIC    HEAT. 


Alcohol  at  0° 0.5475 

Aluminium 0.2122 

Antimony 0.0486 

Bismuth 0.0298 

Brass,  hard 0.0858 

Carbon  disulphide     .     .     .  0.2352 

Copper 0.0933 

Ether  at  0° 0.5290 

Glass,  thermometer  .     .     .  0.1980 

Glycerine 0.5550 

Ice 0.5040 

Iron 0.1124 

Lead .  ,  0.0315 


Mercury 0.0335 

Nitrogen 0.2438 

Olive  oil 0.310 

Oxygen 0.2175 

Platinum 0.0323 

Silver 0.0559 

Salt   . 0.173 

Sulphur 0.1844 

Steel 0.118 

Tin 0.0559 

Turpentine  at  0°  .     .     .     .  0.4106 

Wood  spirit 0.645 

Zinc  .  ,  0.0935 


Table    XIT. 
INDICES    OP    REFRACTION. 


Air 000294 

Aqueous  lens,  eye      .     .       .357 

Alcohol,  ethyl 361 

Benzine 49 

Canada  balsam       ...       .54 
Carbon  disulphide      .     .       .626 

Crown  glass 515 

Crystalline  lens,  eye  .     .       .384 
Diamond      .     .     .  2.47  to  2.75 

Ether 1.354 

Flint  glass    .     .     .  1.57  to  1.71 


Glycerine 

Ice 

Iceland  spar,  ordinary  ray 
"         "      extra,  ray  . 

Quartz,  ordinary  ray  .     . 
"        extra,  ray      .     . 

Rock  salt      .     .     .     .     . 

Ruby 

Vitreous  lens,  eye .     .     . 

Water . 


.47 

.310 

.654 

.483 

.544 

.553 

.550 

.779 

.339 

.332 


These  indices  are  given  for  the  mean  D  lino. 


TABLES    FOE    EEFEEENCE.  371 


Table   XV. 
MENSURATION    RULES. 

Area  of  triangle  =  base  X  h  altitude. 

"      parallelogram  =  base  X  altitude. 

"      trapezoid  =  altitude  X  h  sum  of  parallel  sides. 
Circum.  of  circle  =  diameter  X  3.1416. 
Diameter  of  circle  =  circum.  X  .3183. 
Area  of  circle  =  diameter  squared  X  .7854. 
Area  of  ellipse  =  product  of  diameters  X  .7854. 
Area  of  reg.  polygon  =  sum  of  sides  X  i  apothem. 
Lat.  surface  of  cylinder  =  cir.  base  X  alt. 
Contents  of  cylinder  =  area  base  X  alt. 
Surface  of  sphere  =  diameter  X  circum. 
Contents  of  sphere  =  diameter  cubed  X  .5236. 

Surface  of  pyramid  > 

>  =  cir.  base  X  h  slant  height. 
"         "  cone         } 

Contents  of  cone  =  area  base  X  J  alt. 
Surface  of  frustum  of  pyramid  or  cone  = 

sum  of  cir.  of  bases  X  h  slant  height. 
Contents  of  frustum  of  pyramid  or  cone  = 

J  alt.  X  sum  of  areas  of  bases  and  sq.  rt.  of  product  of  these  areas. 


Table    XVI. 
LENGTH    OF    SECONDS'    PENDULUM. 

Greenwich,  lat.  51°  29' 99.413  cm. 

Paris,                   48°  50' 99-390  " 

New  York,         40°  43'      .     .     .     . 99.317  " 

Washington,       38°  54' 99.306  " 

Lat.          45°  00' 99.356  » 

Equator 99.103  « 

Pole                                           ..........  99.610  » 


372 


PRACTICAL   PHYSICS. 


Table  XVII. 
VELOCITY    OF    SOUND    AT    O°    C. 


Air     ... 
Ash    .... 

Brass  .  .  . 
Caoutchouc 
Carbon  monoxide 
Carbon  dioxide 
Cedar  .  .  . 
Chlorine  .  . 
Copper  .  .  . 
Elm  .... 
Ether  .  .  . 
Fir  .... 
Glass  .... 
Gold  . 


per  sec. 


1,093  ft. 
15,314 

Hydrogen    .     .     per  se 
Iron         .                      " 

c.,  4,163ft 
17  822 

10  885 

Lead  " 

4  030 

197 
1,106 

Maple  .  .  .  .  " 
Oak  " 

13,472 
12  622 

856 
16  503 

Oxygen  .  .  .  .  " 
Pine  " 

1,040 
10  900 

677 
11,666 

Silver  .  .  .  .  » 
Steel  ....." 

8,553 
17  182 

13,516 
3,801 
15,218 
16,488 
5,717 

Tallow  .  .  .  .  " 
Turpentine  at  24°  " 
Walnut  .  .  .  .  " 
Water  at  8.1°  .  " 
Wax  . 

1,170 
3,976 
15,095 
4,708 
2.811 

Tnhle    XVIII. 


ELASTICITY    OF    TRACTION. 


No.  of  kilos,   required  to  double  the  length  of  a  wire  1  sq. 
mm.  in  section. 


Brass       .......  9,000 

Copper 12,400 

Glass,  plate 7,015 

Iron,  wrought 19,000 

Lead 1,800 

Platinum     .     .     .     .     .     .  17,044 


I    Silver     .     .          ....  7,400 

Slate.     .......  11,035 

Steel .  21,000 

Whalebone 700 

Wood      .......  1,100 

Zinc  .     .     .     .     „     .     .     .  8,700 


TABLES    FOft    REFERENCE. 


373 


Table  XIX. 
TENACITY. 


Copper,  drawn 40.3 

"         annealed    .          .     .  30.54 

Iron,  drawn 61.10 

"     annealed     .     .     .     .     .46.88 
Lead,  drawn  ......     2.07 

"      annealed 1.80 

Platinum,  drawn      .      ...  34.10 
"          annealed      .  .23.5 


Silver,  drawn 29.00 

"  annealed  .  .  .  .16.02 

Steel,  drawn 70.00 

"  annealed 40.00 

"  cast,  drawn  .  .  .  .80.00 
"  "  annealed  .  .  .  65.75 

Tin,  drawn 2.45 

"  annealed  1.70 


The  above  table  gives  the  weight  in  kilogrammes  required  to 
break  a  wire  of  the  substance  1  mm.  in  diameter. 

Table    XX. 
TRIGONOMETRICAL    FUNCTIONS. 


Angle. 

Sine. 

Tangent. 

Cotangent. 

Cosine. 

Angle. 

0 

0.000 

0.000 

1.000 

90 

17 

17 

0 

1 

0.017 

0.017 

57.29 

1.000 

89 

18 

18 

1 

2 

0.035 

0.035 

28.64 

0.999 

88 

17 

17 

0 

3 

0.052 

0.052 

19.08 

0.999 

87 

18 

18 

1 

4 

0.070 

0.070 

14.30 

0.998 

86 

17 

17 

2 

5 

0.087 

0.087 

11.43 

0.996 

85 

18 

18 

1 

6 

0.105 

0.105 

9.514 

0.995 

84 

17 

18 

2 

7 

0.122 

0.123 

8.144 

0.993 

83 

17 

18 

3 

8 

0.139 

0.141 

7.115 

0.990 

82 

17 

17 

841 

2 

9 

0.156 

0.158 

6.314 

0.988 

81 

18 

18 

643 

3 

10 

0.174 

0.176 

5.671 

0.985 

80 

17 

18 

526 

3 

11 

0.191 

0.194 

5.145 

0.982 

79 

17 

19 

440 

4 

12 

0.208 

0.213 

4.705 

0.978 

78 

17 

18 

374 

4 

13 

0.225 

0.231 

4.331 

0.974 

77 

17 

18 

320 

4 

14 

0.242 

0.249 

4.011 

0.970 

76 

17 

19 

279 

4 

15 

0.259 

0.268 

3.732 

0.966 

75 

17 

19 

245 

5 

Angle. 

Cosine. 

Cotangent 

Tangent. 

Sine. 

Angle. 

374 


PRACTICAL    PHYSICS. 


Angle. 

Sine. 

Tangent. 

Cotangent. 

Cosine. 

Angle. 

16 

0.276 

0.287 

3.487 

0.961 

74 

16 

19 

216 

5 

17 

0.292 

0.306 

3.271 

0.956 

73 

17 

19 

193 

5 

18 

0.309 

0.32o 

3.078 

0.951 

72 

17 

19 

174 

5 

19 

0.326 

0.344 

2.904 

0.946 

71 

16 

20 

157 

6 

20 

0.342 

0.364 

2.747 

0.940 

70 

16 

20 

142 

6 

21 

0.358 

O.S84 

2.605 

0.934 

69 

17 

20 

130 

7 

22 

0.375 

0.404 

2.475 

0.927 

68 

16 

20 

119 

6 

23 

0.391 

0.424 

2.356 

0.921 

67 

16 

21 

110 

7 

24 

0.407 

0.445 

2.246 

0.914 

66 

16 

21 

101 

8 

25 

0.423 

0.466 

2.145 

0.906 

65 

15 

22 

95 

7 

26 

0.438 

0.488 

2.050 

0.899 

64 

16 

22 

87 

8 

27 

0.454 

0.510 

1.963 

0.891 

63 

15 

22 

82 

8 

28 

0.469 

0.532 

1.881 

0.883 

62 

16 

22 

77 

8 

29 

0.485 

0.554 

1.804 

0.875 

61 

15 

23 

72 

9 

30 

0.500 

0.577 

1.732 

0.866 

60 

15 

24 

68 

9 

31 

0.515 

0.601 

1.664 

0.857 

59 

15 

24 

64 

9 

32 

0.530 

0.625 

1.600 

0.848 

58 

15 

24 

60 

9 

33 

0.545 

0.649 

1.540 

0.839 

57 

14 

26 

57 

10 

34 

0.559 

0.675 

1.483 

0.829 

56 

15 

25 

55 

10 

85 

0.574 

0.700 

1.428 

0.819 

5o 

14 

27 

52 

10 

33 

0.588 

0.727 

1.376 

0.809 

54 

14 

27 

49 

10 

37 

0.602 

0.754 

1.327 

0.799 

68 

14 

27 

47 

11 

88 

0.616 

0,781 

1.280 

0.788 

52 

13 

29 

45 

11 

39 

0.629 

0.810 

1.235 

0.777 

51 

14 

29 

43 

11 

40 

0.643 

0.839 

1.192 

0.766 

50 

13 

30 

42 

11 

41 

0.656 

0.869 

1.150 

.  0.755 

4'J 

13 

31 

39 

12 

42 

0.669 

0.900 

1.111 

0.743 

48 

13 

33 

39 

12 

43 

0.682 

0.933 

1.072 

0.731 

47 

13 

33 

36 

12 

44 

0.695 

0.966 

1.036 

0.719 

46 

12 

34 

36 

12 

45 

0.707 

1.000 

1.000 

0.707 

45 

Angle. 

Cosine. 

Cotangent 

Tangent. 

Sine. 

Angle. 

TABLES    FOE    REFERENCE. 


375 


Table  XXI. 
SOME    USEFUL    NUMBERS. 


7t  =  3.1415926. 
Dyne  in  grammes  =  .00102. 
Poundal  in  dynes  =  13825.  - 
Erg  in  gramme-centimetres  = 

.00102. 
Foot-pound  in  kilogramme-metres 

=  .13825. 

Kilogramme-metre  in  foot-pounds  = 
7.23308. 

Foot-poundal  in  ergs  =  421390. 
\/~2~  =  1.4142. 
A/IT  —  1.7320. 
\/T~  =  2.2361. 
A  cubic  foot  of  water  at  4°  C. 

weighs  in  pounds '=    62.425. 
A  cubic  foot  of  water  at  16f°  C. 

weighs  in  pounds   =  62.321. 


A  cubic  foot  of  air  at  0°  C. 

weighs  in  pounds  =  0.080728. 
1  litre  of  H.  at  0°  C.,    760   mm., 

weighs  0.08969  g. 
1  Paris  foot     =  0.32484  metres. 
1     "•     line      =  2.2588  mm. 
1  Eng.  foot      =  0.30479  m. 
1  Ger.  mile      =  7.4204  kilom. 
1  Eng.  mile      =  1.60929  kilom. 
1  Rhenish  ft.   =  0.31385  m. 
1  metre  =  3.2809  Eng.  ft. 

1  kilometer      =  0.62138  Eng.  mile. 
1  litre  =  0.22017  gal. 

1     "  =  1.76133  pints. 

1  kilogramme  =  2.20462  Ibs. avoir. 
1  gramme         =15.43235  grains. 
1  metre  =39.37  in. 

1  U.  S.  gal.      =231  cu.  in. 


Table   XXII. 
WEIGHTS    AND    MEASURES. 

MEASURES  OF  LENGTH,  ENGLISH. 
1  mi.  =  8  fur.  =  320  rods  =  1760  yd.  =  5280  ft.  =  63360  in. 

MEASURES  OF  LENGTH,  FRENCH. 
1  kilo.  =  1000  m.  =  10000  dcm.  =  100000  cm.  =  1000000  mm. 

MEASURES  OF  SURFACE,  ENGLISH. 
1  acre  =  4840  sq.  yd.  =  43560  sq.  ft. 

MEASURES  OF  SURFACE,  FRENCH. 

1  sq.  H  km.  =  10  sq.  P  km.  =  100  sq.  m.  =  1000  sq.  dcm.  =  10000  sq.  cm. 
=  100000  sq.  mm. 

1  are  =  100  sq.  metres. 


876  PRACTICAL   PHYSICS. 

MEASURES  OF  VOLUME,  ENGLISH. 
1  cu.  yd.  =  27  cu.  ft.  =  46656  cu.  in. 

MEASURES   OF  VOLUME,  FRENCH. 
1  cu.  metre  =  1000  cu.  dcm.  =  1000  litres  =  1000000  ccm. 

ENGLISH  WEIGHTS. 

1  Ib.  avoir.  =  16  oz.  =  256  dr.  =  7000  gr. 

1  oz.  =  437.5  gr. 

FRENCH  WEIGHTS. 
1  kilo.  g.  =  1000  g.  =  10000  dcg.  =  100000  eg.  =  1000000  nig. 

MISCELLANEOUS. 
• 

Lineal  feet  X  -00019  =  miles. 

Square  inches  X  .007  =  sq.  ft. 

Cu.  inches  X  .00058  =  cu.  ft. 

Cu.  ft.  X  7.48  =  TJ.  S.  gallons. 

Cu.  in.  X  . 004329  =U.  S.  gallons. 

IT.  S.  gals.  X  .  13367  =  cu.  ft. 

Cu.  ft.  of  water  X  62.5  =  lbs.  avoir. 

Cu.  in.  of  water  X  .03617  =  lbs.  avoir. 

Metres  X  3.2809  =  ft. 

Ft.  X  0.3048  =  metres. 

Sq.  in.  X  6.451  =  scm. 

Scm.  X  0.155  =  sq.  in. 

Cu.  in.  X  16.386  =  ccm. 

Ccm.  X  .06103  =  cu.  in. 

Litres  X  61.027  —  cu.  in. 

Oz.  avoir.  X  28.35  =  grammes. 

Lb.  X  453.593  =  grammes. 

Gr.  X  15.432  =  grains. 

Kilog.  X  2.2046  =  Ibs.  avoir. 


INDEX. 


INDEX. 


[The  numbers  refer  to  the  articles.] 


Aberration,  spherical,  537,  548. 
Absorption,  of  air  by  water,  52  ;  of 

heat  by  substances,  table,  page 

367. 
Acceleration  due  to   gravity,    131 ; 

table,  page  367. 
Adhesion,  64,  65. 
Air-pump,  experiments   with,  152- 

154,    160-162,    178,    185,    251, 

261 ;  mercury,  163. 
Air-thermometer,  240,  258. 
Amalgam,  electric,  614. 
Amalgamating  battery-zincs,  611. 
Analysis  of  white  light,  551. 
Aneroid  barometer,  159. 
Angle,  critical,  541 ;  measurement 

of,  18  ;  of  prism,  522. 
Angular  currents,  laws  of,  382,  383. 
Apparatus  for  laboratory,   list  of, 

595. 

Archimedes,  principle  of,  180-185. 
Area,  measurement  of,  18,  19. 
Ascent  of  liquids  in  capillary  tubes, 

85  ;  between  plates,  84. 
Astatic  galvanometer,  358. 
Astronomical  telescope,  585. 
Athermancy,  264. 
Atmospheric  pressure,  151-162. 
Attraction,   electrical  law  of,  312; 

magnetic     law    of,     287;     of 

vibrating  bodies,  496-498. 
Atwood's  machine,  130. 
Aurora-tube,  402. 


Balance,  beam,  how  to  use,  23; 
Jolly's,  how  to  make  and  use, 
23. 

Barometer,  158-159. 

Baroscope,  185. 

Batteries,  care  of,  613;  connecting 
together,  369;  galvanic,  346- 
348  ;  for  laboratory,  595. 

Battery,  Daniell's,  358,595;  float- 
ing, 383 ;  fluid  for  carbon,  612  ; 
Gre  let,  595  ;  measure  electro- 
motive force  of,  371-373; 
measure  resistance  of,  367-369  ; 
secondary  or  storage,  408-409; 
table  of  E.  M.  F.  of,  page  365 ; 
thermo-electric,  406. 

Beam-compass,  15. 

Beats,  459,  460,  462. 

Boiling-point  of  liquids,  254;  in- 
fluence of  substance  in  so- 
lution, 255;  of  pressure,  251, 
252,  254;  on  thermometers, 
246 ;  table  of,  page  368. 

Books  of  reference  for  laboratory, 
594. 

Boyle,  law  of,  165. 

Branch  currents,  375. 

Bridge,  Wheatstone's,  358. 

Bunsen's  photometer,  516. 

Buoyancy  of  fluids,  180-185. 

Calibration  of  galvanometer,  374, 
376. 


380 


INDEX. 


Caliper,  inside,  13;  micrometer,  1); 
outside,  12;  verniered  steel,  6. 

Calorimetry,  269-276. 

Camphor,  motion  of,  82. 

Candle-power,  measurement  of, 
517,  518. 

Capillarity,  table  of,  page  361. 

Capillary  action,  77-85;  laws  of, 
85 ;  measure  diameter  of  tube, 
34. 

Carbonic  acid,  testing  room  for, 
231 ;  velocity  of  sound  in,  435. 

Cartesian  diver,  184. 

Cements,  607. 

Centre  of  mass,  117-119;  of  oscil- 
lation, 139 ;  of  percussion,  141. 

Charge  of  Leyden  jar,  not  in  metal, 
340 ;  residual,  335. 

Charging  Leyden  jars,  335-340. 

Chemical  effects  of  electrical  cur- 
rents, 353-355. 

Chladni's  plates,  491. 

Chromic  acid  solution  for  batteries, 
612. 

Circuit,  divided,  law  of,  375. 

Cleavage,  70. 

Coefficient  of  expansion,  234,  235, 
241 ;  table  of,  page  36S. 

Coercive  force,  298. 

Cohesion,  61-71;  figures,  80;  of 
liquids,  64;  of  solids,  61,  62. 

Coil,  induction,  394 ;  resistance, 
358. 

Cold,  artificial  production  of,  277- 
283. 

Collision  of  bodies,  113-116. 

Color,  557-566 ;  complementary, 
561-566;  mixed,  561,  562;  pro- 
duced by  diffraction,  578,  579  ; 
by  pressing  two  plates  together, 
516;  by  polarized  light,  590- 


593;  simple,  551-552;  un- 
equally refrangible,  553. 

Commutator,  to  make,  347. 

Compound  microscope,  584;  po- 
larizing attachment,  592. 

Concave  lenses,  546-548;  mirrors, 
532,  534,  535,  537. 

Condensers,  332-340. 

Conduction  of  heat,  215-223,  page 
367;  electricity,  318,  page  364; 
of  sound,  428-432. 

Conductometer,  217,  219. 

Conductors,  distribution  of  electri- 
fication on,  325-331. 

Cone,  volume  of  frustum  of,  22. 

Controlling  magnet  for  galvanom- 
eter, 365. 

Convection  of  heat,  225-231. 

Convex  lenses,  545,  547-549;  mir- 
rors, 533,  534,  536. 

Cooling,  affected  by  character  of 
surface,  265 ;  Newton's  law  of, 
267. 

Corks,  boring  holes  in,  595. 

Critical  angle,  541. 

Crova's  disk,  439. 

Crystallization,  66-70;  increase  of 
volume  due  to,  242-244. 

Cube,  Leslie's,  258. 

Current  electricity,  345-356  ;  extra, 
395 ;  induced,  386-397. 

Curved  mirrors,  532-537. 

Curvilinear  motion,  125-127. 

Cylindrical  jar,  to  measure,  13. 

Daniell's  battery,  358,  595. 

Dark  lines  of  solar  spectrum,  568, 

569. 
Density,  determination  of ,  187-198; 

of  ice,  244 ;  table  of,  page  361. 
Deviation,  angle  of,  540. 


INDEX. 


381 


Diagonal  scale,  2. 

Dialyzer,  101. 

Diameter  of  wires,   table  of,  page 

365. 

Diapason,  459. 
Diathermancy,  264. 
Differential  thermometer,  258. 
Diffraction  of  light,  578-581. 
Diffusion,  95-106;  fountain,  102. 
Dip  of  needle,  306. 
Direction  of  current,  347,  348. 
Discharger,  jointed,  335. 
Discord,  487-489. 
Dispersion  of  light,  551. 
Distillation,  256. 
Distribution  of  electrification,  324- 

331;  of  magnetism,  301. 
Divided  currents,  375. 
Dividers,  2;  proportional,  1(1. 
Divisibility  of  matter,  44-47. 
Double  refraction,  589. 
Drop-size  of  liquids,  63. 
Duration  of  electric  spark,  344. 
Dust  figures,  425. 

Elasticity,  73-76 ;  table  of  limits  of, 
page   364;    of   traction,    table,    ' 
page  372. 

Electric  amalgam,  614 ;  attraction  I 
and  repulsion,  309-314;  con-  ! 
ductivity,  318;  motor,  388. 

Electrical     condensers,      333-340; 
conductivity,     318,   page    364 ; 
conductivity   affected  by  heat, 
364;      urrents,     direction    of,    j 
347,  348;  currents,  division  of ,    I 
376 ;   currents,  effects  of,  350- 
356;      distribution,     325-331;    ! 
machines,  cleaning,  615;  meas-    I 
urements,  358-376  ;  pistol,  352  ; 
resistance,  table  of,  page  365. 


Electricity,  308-409;  current,  345- 
356;  developed  by  chemical 
action,  346-348 ;  developed  by 
friction,  308-342  ;  developed  by 
heat,  406 ;  developed  by  in- 
duction, 343,  344,  386-397. 

Electrification  detected,  315-317. 

Electrolysis,  353-355. 

Electrodynamics,  378-384;  magnet, 
382 ;  magnetism,  378-384. 

Electro-motive  force.  370-373 ;  table 
of,  page  365 

Electrophorus,  343. 

Electroscope,  315. 

Equilibrium  of  forces,  109-112;  of 
liquids,  169;  of  bodies,  120- 
122. 

Erdmann's  float,  20. 

Expansion,  coefficient  of,  234,  239, 
241;  cubical,  235,  239,  241; 
table  of,  page  368 ;  on  crys- 
tallization, 242-244;  of  gases, 
240,  241 ;  of  liquids,  238,  239  ; 
of  gases  producing  cold,  207, 
281 ;  by  heat,  233-244. 

Extra  current,  395. 

Evaporation,  cold  due  to,  279,  280. 

Eye,  model  of,  583. 

Falling  bodies,  law  of,  133;  inde- 
pendent of  mass,  133. 

Films,  soap,  81,  577. 

Fire-syringe,  201. 

Flask,  specific  gravity,  190. 

Flexure,  elasticity  of,  75. 

Float,  Erdmann's,  20. 

Floating  battery,  383. 

Flotation,  principle  of,  183. 

Fluids,  buoyant  force  of,  181-185; 
mechanics  of,  149-198;  pres- 
sure in,  150-163. 


382 


INDEX. 


Focal  distance  of  lenses,  545-546; 
of  spherical  mirrors,  535-536. 

Force,  acceleration  due  to  con- 
stant, 129-131;  buoyant,  180- 
185;  coercive,  298;  electro- 
motive, 371-373  ;  lines  of  mag- 
netic, 300,  379,  381;  measure 
effect  of  a,  132. 

Forces,  composition  of,  109-112; 
parallel,  112. 

Fountain,  Hero's,  177;  intermit- 
tent, 176  ;  in  vacuo,  162. 

Fraunhofer's  lines,  568,  569. 

Freezing  mixtures,  277,  278,  283. 

Friction,  142. 

Frictional  plate  machine,  342. 

Fusion,  latent  heat  of,  275. 


Galilean  telescope,  586. 

Galvanometer,  calibration  of,  374, 
376  ;  resistance  of,  365  ;  simple, 
to  make,  347 ;  tangent,  to  make, 
358. 

Gases,  cold  produced  by  expansion 
of,  207,  281;  compressibility 
of,  165 ;  density  of,  page  363 ; 
endosmose  of,  102-106 ;  ex- 
pansibility of,  160 ;  thermal 
conductivity  of,  261 ;  velocity 
of  sound  in,  434-436. 

Gassiot's  cascade,  403. 

Glass,  bending  tube,  602 ;  cutting, 
600 ;  closing  end  of  tube,  603  ; 
drawing  on,  606 ;  drawing  out 
tube,  604 ;  drilling  holes  in, 
605  ;  silvering,  608  ;  smoothing 
end  of  tube,  601. 

Graphic  method,  598;  study  of 
sound,  500,  501. 

Grating,  Nobert's,  578-579. 


Gravitation,  129-131;  acceleration 
due  to,  131 ;  table,  page  367. 

Haldat's  apparatus,  168. 

Hardness,  Mohr's  scale,  71. 

Harmony,  487-489. 

Heat,  199-283 ;  absorption  of,  263, 
264  ;  capacity  of  substance  for, 
271-274;  capacity  of  water  for, 
269,  270;  conduction  of,  215- 
223;  convection  of,  224-231; 
converted  into  mechanical  mo- 
tion, 207-210;  due  to  chemical 
action,  212-214;  due  to  electric 
currents,  350-352 ;  due  to  me- 
chanical motion,  207-210;  ex- 
pansion by,  233-244;  law  of 
reflection  of,  262;  latent,  of 
water,  275;  latent,  of  steam, 
276;  radiant,  258-267;  radi- 
ation of,  affected  by  surface, 
265 ;  radiation  of,  affected  by 
temperature  of  surrounding  air. 
267;  specific,  272-274;  table 
of  absorbing,  conducting,  radi- 
ating, reflecting  power,  page 
367 ;  table  of  latent,  page  369  ; 
table  of  specific,  page  370. 

Hemispheres,  Magdeburg,  154. 

Hero's  fountain,  177. 

Holtz  machine,  344. 

Hydrometer,  Beaume's,  196;  Nich- 
olson's, 193,  195. 

Images,  after,  563-566 ;  formed  by 
lenses,  548;  formed  by  mir- 
rors, 528-531,  534;  multiple, 
530,  531;  through  small  aper- 
tures, 511,  512. 

Impenetrability,  36-42 

Inclined  plane,  148 


INDEX. 


383 


Indestructibility,  58,  59. 

Index  of  refraction,  539,  540 ;  table 

of,  page  370. 
Induction,  coil,  391,  394;  current, 

386-397 ;  current  on  itself,  395  ; 

earth,  397;  magnetic,  291,  292, 

307 ;  statical,  320-323. 
Inelastic  bodies,  113. 
Interference  of  light,  by  diffraction, 

578-579;    by    reflection,    57(5, 

577,  581;   of   sound,    457-462, 

492-494. 

Intermittent  fountain,  176. 
Irregular  reflection,  523,  524. 


Jar,  Leyden,  335-340. 

Jet,  height  of,  170,  175,  177. 

Jet-tube,  to  make,  604. 

Jolly's  balance,  23. 

Juriirs  laws  of  capillarity,  85. 


Konig's  manometric  flames,  502. 
Kundt's    method  of   measuring  ve- 
locity of  sound,  437. 


Laboratory  note-book,  597;  oper- 
ations, 600-615 ;  physical,  594- 
599;  room,  594;  rules,  599; 
work,  conducting,  596. 

Lantern,  magic,  509. 

Latent  heat,  of  steam,  276 ;  of 
water,  275 ;  of  liquefaction  and 
vaporization,  table,  page  369. 

Lateral  jets,  150. 

Lenses,  foci  of  concave,  546;  foci 
of  convex,  545 ;  effect  on 
pencils  of  light,  547  ;  magnify- 
ing power  of,  549;  spherical 
aberration,  548. 


Leslie's  cube,  258. 

Lever,  144-145. 

Leyden  jar,  charging,  335,337-339  ; 
charging  by  induction  coil,  396 ; 
connecting  two  or  more  to- 
gether, 336 ;  discharging,  335 ; 
to  make,  336;  office  of  coat- 
ings, 340;  residual  charge,  335; 
spangled,  399. 

Liebig's  condenser,  256. 
!  Light,  598-593;  amount  of  light 
reflected,  525,  526;  diffused 
reflection  of,  523,  524;  dis- 
persion of,  550-556 ;  double 
refraction  of,  538-543;  inter- 
ference of,  575-581 ;  law  of 
intensity  of,  515,  516;  multiple 
reflection  of,  530,  531 ;  polari- 
zation of,  588-593 ;  rectilinear 
propagation  of,  510-513;  re- 
flected, amount  of,  525,  526; 
reflection  of,  519-526;  re- 
fraction of,  538-543;  regular 
reflection  of,  520-522;  single 
refraction  of,  538-543;  total 
reflection  of,  541-543. 

Linear  expansion,  coefficient  of, 
234 ;  table,  page  368. 

Liquids,  buoyancy  of,  180-184; 
conductivity  of  heat  by,  222, 
223;  diffusion  of,  95-101; 
equilibrium  of,  169  ;  expansion 
of,  228,  229;  manner  of  heat- 
ing, 225,  226 ;  pressure  inde- 
pendent of  shape  of  vessel,  168 ; 
specific  heat  of,  274 ;  transmit 
pressure,  167. 

Lissajou's  curves,  503. 

Loudness  of  sound,  447-456. 

Luminous  effects  of  electric  dis- 
charge, 344,  393,  398-404. 


384 


INDEX. 


Machines,  electrical,  341-344; 
simple,  144-148. 

Magic  lantern,  509;  slides,  606. 

Magnetic  effects  of  electric  cur- 
rents, 356 ;  field,  300-304  ;  field 
around  conductors  carrying 
current,  378,  379,  381;  in- 
duction, 291,  292,  307;  trans- 
parency, 289,  290. 

Magnetism,  284-307;  nature  of, 
294-296;  terrestrial,  306,307. 

Magnetizing,  by  currents,  356,  382  ; 
by  divided  touch,  301;  by 
earth,  307;  by  induction,  292. 

Magnetoscope,  Coulomb's,  301. 

Magnets,  effects  of  heating,  296 ; 
effects  of  jarring,  295;  electro, 
382;  induction  by,  291,  292; 
polarity  of,  286-288  ;  to  make, 
285,  301. 

Magnify  ing-power,  549,  587. 

Manometric  flames,  502. 

Mass,  centre  of,  118,  119;  esti- 
mation of,  23-34. 

Matter,  properties  of,  1-106. 

Measurement,  angular,  17,  18; 
linear,  2-17  ;  of  candle-power, 
517,  518;  of  electro-motive 
force,  370-373;  of  effect  of 
force,  132;  of  focal  distance, 
535,  536,  545,  546;  of  magni- 
fying-power,  549,  587;  of 
mass,  23-34;  of  resistance, 
357-369  ;  of  surface,  18, 19  ;  of 
velocity  of  sound,  434-437 ;  of 
vibration-number,  472,  473 ; 
of  volume,  20-22. 

Mechanics,  of  fluids,  149-198 ;  of 
solids,  107-148. 

Melde's  experiments  with  vibrating 
strings,  477. 


Melting-point  of  substances,  253, 
table  of,  page  369. 

Mensuration  rules,  table  of,  page 
371. 

Mercury,  cleaning,  609. 

Micrometer  caliper,  9. 

Microphone,  390. 

Microscope,  584. 

Mirrors,  curved,  532-537  ;  effect  on 
pencils  of  light,  532,  533  ;  plane, 
528-531 ;  measure  focal  dis- 
tance of  concave,  535  ;  measure 
focal  distance  of  convex,  536. 

Mixtures,  freezing,  283. 

Motion,  laws  of,  108-116;  accel- 
erated, 129-131 ;  curvilinear, 
124-127;  reflection  of,  116; 
wave,  411-417. 

Multiple  images,  530,  531. 

Needle,  dipping,  306. 

Newton's  color  disk,  344,  561 ;  law 
of  cooling,  267;  rings,  576. 

Nicholson's  hydrometer,  193,  195. 

Nicol  prism,  591. 

Nobert's  grating,  579. 

Nodes  of  organ  pipe,  485,  486 ;  of 
vibrating  plates,  491 ;  of  vibrat- 
ing strings,  481. 

Norremberg's  doubler,  to  make, 
591. 

Note-book,  laboratory,  597. 

Oersted's  parallelogram,  347. 

Ohm's  law,  358. 

Optical  instruments,  582-587 ;  Ltudy 

of  sound,  502,  503. 
Optics,  508-593. 
Osmose,  99-105. 
Overtones,  478-481. 


INDEX. 


385 


Paradox,  122,  168,  252. 

Parallel  forces,  112. 

Parallelogram  of  forces,  109-11 1. 

Pascal,  law  of,  167-170. 

Pendulum,  Blackburn's  sand,  504  ; 
law  of,  137-141;  table  of 
lengths  of  seconds,  page  371. 

Percussion,  heat  developed  by,  200. 

Photometry,    514-518. 

Pitcli  of  sound,  471-473. 

Plates,  ascension  of  liquids  between, 
84;  Chladni's,  491;  tourmaline, 
590;  vibration  of  plates,  491- 
494. 

Point,  boiling,  254 ;  affected  by 
pressure,  251-254;  affected  by 
substances  in  solution,  255 ; 
located  on  thermometer,  246. 

Polariscope,  to  make,  591;  micro- 
scope attachment,  592. 

Polarity  of  magnets,  285-288. 

Poles,  strength  compared,  302. 

Polygon,  measure  area  of,  19. 

Porosity,  49-54. 

Porte  lumiere,  to  make,  509. 

Powders,  density  of,  192. 

Pressure,  depends  on  depth,  150, 
155 ;  effect  on  boiling-point, 
254 ;  elasticity  manifested  by , 
73;  exerted  by  atmosphere,  j 
151-163;  exerted  in  every  di- 
rection, 154,  155,  167;  inde- 
pendent of  form  of  vessel, 
168 ;  on  a  body  in  a  fluid,  180- 
185. 

Principle  of  Archimedes,  179-185. 

Prism,  measure  angle  of,  522  ;  make 
carbon  disulphide,  551 ;  meas- 
sure  refraction  of,  540 ;  Nicol, 
591, 

Projectiles,  134,  135. 


Proof-plane,  316. 

Propagation  of  sound,  439. 

Protractor,  17. 

Pulley,  146;  mass  determined,  130. 

Pump,   air,  152-154,   160-1G2,  178, 

185,   251,   261;   mercury,   163; 

suction,  178. 
Pyrometer,  209,  234. 

Radiant  heat,  257-267;  causes 
which  modify,  263-266;  in- 
tensity of,  259 ;  law  of  reflec- 
tion, 262. 

Radiating  power,  causes  which 
modify,  265-267. 

Radiometer,  210. 

Rainbow,  project  on  screen,  556. 

Reflection,  laws  of,  116,  262,521; 
irregular,  523-524 ;  regular, 
519-522;  of  heat,  262;  of 
light,  519-526 ;  of  sound,  440- 
443. 

Refraction,  double,  589;  index  of, 
539,  540;  single,  538-543;  of 
sound,  440-446;  table  of  in- 
dices, page  370. 

Residual  charge,  335. 

Resistance,  coils,  358 ;  of  batteries, 
367-369 ;  of  conductors,  358- 
364  ;  of  galvanometers,  365. 

Resonating  air-columns,  effect  of 
diameter  on  length  of,  454. 

Resonators,  455,  456. 

Resultant  of  forces,  109-112. 

Rheostat,  358. 

Rider,  23. 

Rings,  Newton's,  576. 

Rods,  law  of  vibrating,  475;  meas- 
ure length  of,  6. 

Rumford's  photometer,  517. 


386 


INDEX. 


Scale,  accuracy  tested,  15;  copy  a, 
14 ;  diagonal,  2 ;  of  hardness,  71. 

Sciopticon,  509. 

Secondary  batteries,  408,  409. 

Shadows,  513. 

Shunt,  374-370. 

Singing  flame,  426. 

Siphon,  172-177. 

Siren,  472. 

Soap-film,  colors  of,  577;  solution, 
to  make,  80;  strength  of,  81. 

Soldering,  610. 

Solenoid,  action  of  currents  on, 
382 ;  of  magnets  on,  382. 

Solubility,  87-93. 

Sonometer;  476. 

Sound,  410-507 ;  attending  magne- 
tization and  demagnetization, 
356  ;  graphic  and  optical  study 
of,  499-504 ;  interference  of, 
457-462,  492,  493 ;  loudness  of, 
447-456  ;  pitch,  471-473  ;  propa- 
gation of,  438,  439  ;  reflection 
of,  440-443 ;  refraction  of,  444- 
446;  sources  of,  418-426; 
transmission  of,  427-432 ;  ve- 
locity of,  433-437;  table  of 
velocities,  page  372. 

Sounding  air-columns,  482-486. 

Spar,  Iceland,  589. 

Specific  heat,  272-274;  table  of, 
page  370. 

Spectroscope,  522;  to  make,  569. 

Spectrum,  absorption,  571-573;  an- 
alysis, 567-574;  bright  line, 
570,  574;  colors,  pure,  552; 
color  unequally  refrangible, 
553;  dark  line,  568,  571-573; 
diffraction,  578-580;  mapping, 
569 ;  solar,  to  project  on  screen, 
551. 


Sphere,  measure  diameter  of,  12. 
Spherical  aberration,  537,  548. 
Spherometer,  11. 
Sprengel's  air-pump,  163. 
Springs,  intermittent,  176. 
Stability,  120-123. 
Stable  equilibrium,  120,  121. 
Storage  batteries,  408,  409. 
Strength  of  substances,  62. 
Strings,  laws  of,  476,  477. 
Suction  pump,  178. 
Surface  tension,  78-82. 
Sympathetic  vibrations,  463-470. 
Syringe,  fire,  201. 

Table,  laboratory,  594  ;  to  measure, 
5;  reference,  page  361-376. 

Tangent  galvanometer,  358. 

Telegraph  line,  384. 

Telephone,  acoustic,  430;  electric, 
389. 

Telescope,  astronomical,  585  ;  Gali- 
lean. 586 ;  magnifying  power 
of,  587 ;  terrestrial,  585. 

Temperature  of  boiling-point  of 
water,  247,  251 ;  of  substances, 
216,  249. 

Tenacity,  62,  74 ;  table  of,  page  373. 

Terrestrial,  gravitation,  129-132; 
magnetism,  305-307 ;  telescope, 
585. 

Thermal  capacity  of  substances, 
272-274. 

Thermo-electricity,  406. 

Thermometer,  accuracy  of  location 
of  standard  points,  246;  air- 
thermometer,  258 ;  comparison 
with  standard,  250;  displace- 
ment of  zero,  248. 

Thermometry,  246-256. 

Thermopile,  259. 


INDEX. 


387 


Thermoscope,  240. 
Thickness,  to  measure,  9-11. 
Tools  for  laboratory,  594. 
Torsion,  elasticity  of,  76. 
Tourmaline  tongs,  590. 
Traction,  elasticity  of,  table,  page 

372. 

Transmission  of  sound,  427-432. 
Triangle,  measure,  area  of,  18. 
Trigonometrical  functions,  table  of, 

page  373. 
TyndalFs    experiment    on    specific 

heat,  273. 

Unstable  equilibrium,  121,  122. 
Useful  numbers,  table  of,  page  375. 

Velocity  of  sound,  433-437 ;  table, 

page  372. 

Ventilation,  227-231. 
Vernier,  6. 

Vibrating,    bodies,    attraction    of, 
•    496-498  ;  plates  and  bells,  490- 

495;  rods,   475;    strings,    476, 

477. 
Vibration,    number,    to    measure, 

472,  473. 
Vibrations,  sympathetic,  463-470. 


Vocal  organs,  505-507. 

Volume,  of  irregular  objects,  20; 
regular  objects,  13,  22;  sub- 
stances soluble  in  water,  21. 

Water-hammer,  TyndalPs  adhesion, 

65. 

Wave  motion,  411-417. 
Weighing,  manner  of,  24 ;  problems 

in,  25-34. 
Weights,    centigramme,  to    make, 

33. 
Weights    and    measures,  table   of, 

page  375. 

Wheatstone's  bridge,  358. 
Wheel  and  axle,  147. 
Whirling-machine,  125. 
White  light,  decomposition  of,  551. 
Wire-gauge,  9 ;    measure   diameter 

of,  9 ;  measure  resistance   of, 

357-364. 
Wood,    thermal     conductivity    of, 

221 ;    transmission    of     sound 

by,    429;     velocity    of    sound 

measured,  437. 

Zero,  displacement  of,  248. 
Zinc,  amalgamation  of,  611. 


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